Solved: (I) Four 1.50-V cells are connected in series to a

Calculate the terminal voltage for a battery with an internal resistance of \(0.900~\Omega\) and an emf of 6.00 V when the battery is connected in series with \((a)\) a 71.0-\(\Omega\) resistor, and \((b)\) a 710-\(\Omega\) resistor. Equation Transcription: Text Transcription: 0.900 Omega 71.0-Omega 710-Omega

Four 1.50-V cells are connected in series to a 12.0-\(\Omega\) lightbulb. If the resulting current is 0.45 A, what is the internal resistance of each cell, assuming they are identical and neglecting the resistance of the wires? Equation Transcription: Text Transcription: Omega

What is the internal resistance of a 12.0-V car battery whose terminal voltage drops to 8.8 V when the starter motor draws 95 A? What is the resistance of the starter?

A 650-\(\Omega\)and an 1800-\(\Omega\) resistor are connected in series with a 12-V battery. What is the voltage across the 1800-\(\Omega\) resistor? Equation Transcription: Text Transcription: 650-Omega 1800-Omega 1800-Omega

Three 45-\(\Omega\) lightbulbs and three 65-\(\Omega\) lightbulbs are connected in series. \((a)\) What is the total resistance of the circuit? \((b)\) What is the total resistance if all six are wired in parallel? Equation Transcription: Text Transcription: 45-Omega 65-Omega

Suppose that you have a 580-\(\Omega\), a 790-\(\Omega\), and a 1.20-k\(\Omega\) resistor. What is \((a)\) the maximum, and \((b)\) the minimum resistance you can obtain by combining these? Equation Transcription: Text Transcription: 580-Omega 790-Omega 1.20-k Omega

How many 10-\(\Omega\) resistors must be connected in series to give an equivalent resistance to five 100-\(\Omega\) resistors connected in parallel?

(II) Design a “voltage divider” (see Example 19–3) that would provide one-fifth (0.20) of the battery voltage across \(R_2\), Fig. 19-6. What is the ratio \(R_1/R_2\)?

Suppose that you have a 9.0-V battery and wish to apply a voltage of only 3.5 V. Given an unlimited supply of 1.0-\(\Omega\) resistors, how could you connect them to make a “voltage divider” that produces a 3.5-V output for a 9.0-V input? Equation Transcription: Text Transcription: 1.0-Omega

Three 1.70-k\(\Omega\) resistors can be connected together in four different ways, making combinations of series and/or parallel circuits. What are these four ways, and what is the net resistance in each case? Equation Transcription: Text Transcription: 1.70-k Omega

A battery with an emf of 12.0 V shows a terminal voltage of 11.8 V when operating in a circuit with two lightbulbs, each rated at 4.0 W (at 12.0 V), which are connected in parallel. What is the batterys internal resistance

Eight identical bulbs are connected in series across a 120-V line. (a) What is the voltage across each bulb? (b) If the current is 0.45 A, what is the resistance of each bulb, and what is the power dissipated in each?

Eight bulbs are connected in parallel to a 120-V source by two long leads of total resistance \(1.4~\Omega\). If 210 mA flows through each bulb, what is the resistance of each, and what fraction of the total power is wasted in the leads? Equation Transcription: Text Transcription: 1.4 Omega

(II) A close inspection of an electric circuit reveals that a \(480-\Omega\) resistor was inadvertently soldered in the place where a \(350-\Omega\) resistor is needed. How can this be fixed without removing anything from the existing circuit?

Eight 7.0-W Christmas tree lights are connected in series to each other and to a 120-V source. What is the resistance of each bulb?

Determine \((a)\) the equivalent resistance of the circuit shown in Fig. 19–48, \((b)\) the voltage across each resistor, and \((c)\) the current through each resistor.

A 75-W, 120-V bulb is connected in parallel with a 25-W, 120-V bulb. What is the net resistance?

\((a)\) Determine the equivalent resistance of the “ladder” of equal 175-\(\Omega\) resistors shown in Fig. 19–49. In other words, what resistance would an ohmmeter read if connected between points A and B? \((b)\) What is the current through each of the three resistors on the left if a 50.0-V battery is connected between points A and B?

What is the net resistance of the circuit connected to the battery in Fig. 19–50?

(II) Calculate the current through each resistor in Fig. 19–50 if each resistance \(R=3.25~\mathrm k \Omega \) and \(V=12.0~ \mathrm V\). What is the potential difference between points A and B? Equation Transcription: Text Transcription: R=3.25 k Omega V=12.0 V

(III) Two resistors when connected in series to a 120-V line use one-fourth the power that is used when they are con- nected in parallel. If one resistor is \(4.8~ \mathrm k \Omega\), what is the resistance of the other? Equation Transcription: Text Transcription: 4.8 k Omega

Three equal resistors \((R)\) are connected to a battery as shown in Fig. 19–51. Qualitatively, what happens to \((a)\) the voltage drop across each of these resistors, \((b)\) the current flow through each, and \((c)\) the terminal voltage of the battery, when the switch S is opened, after having been closed for a long time? \((d)\) If the emf of the battery is 9.0 V, what is its terminal voltage when the switch is closed if the internal resistance \(r\) \(0.50~ \Omega\) is and \(R=5.50~ \Omega\)? \((e)\) What is the terminal voltage when the switch is open? ________________ Equation Transcription: Text Transcription: 0.50 Omega R=5.50 Omega

(III) A 2.5-k\(\Omega\) and a 3.7-k\(\Omega\) resistor are connected in parallel; this combination is connected in series with a 1.4-k\(\Omega\) resistor. If each resistor is rated at 0.5 W (maximum without overheating), what is the maximum voltage that can be applied across the whole network? Equation Transcription: Text Transcription: 2.5-k Omega 3.7-k Omega 1.4-k Omega

Consider the network of resistors shown in Fig. 19–52. Answer qualitatively: \((a)\) What happens to the voltage across each resistor when the switch S is closed? \((b)\) What happens to the current through each when the switch is closed? \((c)\) What happens to the power output of the battery when the switch is closed? \((d)\) Let \(R_1=R_2=R_3=R_4=155~ \Omega\) and \(V=22.0~\mathrm V\). Determine the current through each resistor before and after closing the switch. Are your qualitative predictions confirmed? ________________ Equation Transcription: Text Transcription: R_1=R_2=R_3=R_4=155 Omega V=22.0 V

Calculate the current in the circuit of Fig. 19–53, and show that the sum of all the voltage changes around the circuit is zero. ________________ Equation Transcription: Text Transcription: r=2.0 Omega 9.5 Omega 14.0 Omega

Determine the terminal voltage of each battery in Fig. 19–54. ________________ Equation Transcription: ?=12 V Text Transcription: r=2.0 r=1.0 R=4.8 E=12 V

For the circuit shown in Fig. 19–55, find the potential difference between points a and b. Each resistor has \(R=160~\Omega\) and each battery is 1.5 V. Equation Transcription: Text Transcription: R=160 Ohms

Determine the magnitudes and directions of the currents in each resistor shown in Fig. 19–56. The batteries have emfs of \(\mathscr E_1=9.0~\mathrm V\) and \(\mathscr E_2=12.0~\mathrm V\) and the resistors have values of \(R_1=25~ \Omega,~R_2=68~ \Omega\), and \(R_3=35~ \Omega\). \((a)\) Ignore internal resistance of the batteries. \((b)\) Assume each battery has internal resistance \(r=1.0~ \Omega\). Equation Transcription: ?1=9.0 V ?2=12.0 V ?1 ?2 Text Transcription: E_1=9.0 V E_2=12.0 V R_1=25 Omega R_2=65 Omega R_3=35 Omega r=1.0 Omega E_1 E_2 R_1 R_2 R_3

\((a)\) What is the potential difference between points a and d in Fig. 19–57 (similar to Fig. 19–13, Example 19–8), and \((b)\) what is the terminal voltage of each battery? ________________ Equation Transcription: Text Transcription: I_1 I_2 47 Omega I_3 34 Omega r=1 Omega E_2=45 V 18 Omega E_1=85 V r=1 Omega

Calculate the magnitude and direction of the currents in each resistor of Fig. 19–58. ________________ Equation Transcription: Text Transcription: 120 Omega 25 Omega 56 Omega 74 Omega 110 Omega

Determine the magnitudes and directions of the currents through \(R_1\) and \(R_2\) in Fig. 19–59. ________________ Equation Transcription: Text Transcription: R_1 R_2 V_1=9.0 V R_1=22 Omega R_2=18 Omega V_3=6.0 V

(II) Repeat Problem 31, now assuming that each battery has an internal resistance \(r=1.4~ \Omega\). Equation Transcription: Text Transcription: r=1.4 Omega

\((a)\) A network of five equal resistors \(R\) is connected to a battery \(\mathscr E\) as shown in Fig. 19–60. Determine the current \(I\) that flows out of the battery. \((b)\) Use the value determined for \(I\) to find the single resistor \(R_\mathrm{eq}\) that is equivalent to the five-resistor network." Equation Transcription: Text Transcription: R_eq

\((a)\) Determine the currents \(I_1\), (I_2\), and (I_3\) in Fig. 19–61.Assume the internal resistance of each battery is \(r=1.0~ \Omega\). \((b)\) What is the terminal voltage of the 6.0-V battery? ________________ Equation Transcription: Text Transcription: I_1,I_2 I_3 r=1.0 Omega 22 Omega 11 Omega 28 Omega 12 Omega 16 Omega I_1 I_2 I_3

(III) What would the current \(I_1\) be in Fig. 19–61 if the 12-\(\Omega \) resistor is shorted out (resistance = 0)? Let \(r=1.0~ \Omega\). ________________ Equation Transcription: Text Transcription: I_1 12-Omega r=1.0 Omega 22 Omega 11 Omega 28 Omega 12 Omega 16 Omega I_1 I_2 I_3

Suppose two batteries, with unequal emfs of 2.00 V and 3.00 V, are connected as shown in Fig. 19–62. If each internal resistance is \(r=0.350~ \Omega\), and \(R=4.00~ \Omega\), what is the voltage across the resistor \(R\)? Equation Transcription: Text Transcription: r=0.350 Omega R=4.00 Omega R=4.00 Omega E=2.00 V E=3.00 V

A battery for a proposed electric car is to have three hundred 3-V lithium ion cells connected such that the total voltage across all of the cells is 300 V. Describe a possible connection configuration (using series and parallel connections) that would meet these battery specifications.

\((a)\) Six 4.8-\(\mu \mathrm F\) capacitors are connected in parallel. What is the equivalent capacitance? \((b)\) What is their equivalent capacitance if connected in series? Equation Transcription: Text Transcription: 4.8-mu F

(I) A 3.00-\(\mu\)F and a 4.00-\(\mu\)F capacitor are connected in series, and this combination is connected in parallel with a 2.00-\(\mu\)F capacitor (see Fig. 19–63). What is the net capacitance? Equation Transcription: Text Transcription: 3.00-mu F 4.00-mu F 2.00-mu F C_1=3.00 mu F C_2=4.00 mu F C_3=2.00 mu F V=21.0 V

If 21.0 V is applied across the whole network of Fig. 19–63, calculate \((a)\) the voltage across each capacitor and \((b)\) the charge on each capacitor. ________________ Equation Transcription: Text Transcription: C_1=3.00 mu F C_2=4.00 mu F C_3=2.00 mu F V=21.0 V

The capacitance of a portion of a circuit is to be reduced from 2900 pF to 1200 pF. What capacitance can be added to the circuit to produce this effect without removing existing circuit elements? Must any existing connections be broken to accomplish this?

(II) An electric circuit was accidentally constructed using a 7.0-\(\mu\)F capacitor instead of the required 16-\(\mu\)F value. Without removing the 7.0-\(\mu\)F capacitor, what can a techni- cian add to correct this circuit? Equation Transcription: Text Transcription: 7.0- mu F 16- mu F 7.0- mu F

(II) Consider three capacitors, of capacitance 3200 pF, 5800 pF, and 0.0100 \(\mu\)F. What maximum and minimum capacitance can you form from these? How do you make the connection in each case? Equation Transcription: Text Transcription: 0.0100 mu F

Determine the equivalent capacitance between points a and b for the combination of capacitors shown in Fig. 19–64. ________________ Equation Transcription: Text Transcription: C_1 C_2 C_3 C_4

What is the ratio of the voltage \(V_1\) across capacitor \(C_1\) in Fig. 19–65 to the voltage \(V_2\) across capacitor \(C_2\)? ________________ Equation Transcription: Text Transcription: C_1 V_1 V_2 C_2 C_2=1.0 mu F C_1=1.0 mu F C_3=1.0 mu F

(II) A 0.50-\(\mu\)F and a 1.4-\(\mu\)F capacitor are connected in series to a 9.0-V battery. Calculate \((a)\) the potential difference across each capacitor and \((b)\) the charge on each. \((c)\) Repeat parts \((a)\) and \((b)\) assuming the two capacitors are in parallel. Equation Transcription: Text Transcription: 0.50- mu F 1.4- mu F

A circuit contains a single 250-pF capacitor hooked across a battery. It is desired to store four times as much energy in a combination of two capacitors by adding a single capacitor to this one. How would you hook it up, and what would its value be?

(II) Suppose three parallel-plate capacitors, whose plates have areas \(A_1\), \(A_2\), and \(A_3\) and separations \(d_1\), \(d_2\), and \(d_3\), are connected in parallel. Show, using only Eq. 17–8, that Eq. 19–5 is valid. Equation Transcription: Text Transcription: A_1 A_2 A_3 d_1 d_2 d_3

(II) Two capacitors connected in parallel produce an equivalent capacitance of 35.0 \(\mu\)F but when connected in series the equivalent capacitance is only 4.8 \(\mu\)F. What is the individual capacitance of each capacitor? Equation Transcription: Text Transcription: 35.0 mu F 4.8 mu F

(III) Given three capacitors, \(C_1=2.0~ \mu \mathrm F\), \(C_2=1.5~ \mu \mathrm F\), and \(C_3=3.0~ \mu \mathrm F\), what arrangement of parallel and series connections with a 12-V battery will give the minimum voltage drop across the 2.0-\(\mu\)F capacitor? What is the minimum voltage drop? Equation Transcription: Text Transcription: C_1=2.0 mu F C_2=1.5 mu F C_3=3.0 mu F 2.0- mu F

In Fig. 19–66, suppose \(C_1=C_2=C_3=C_4=C\). \((a)\) Determine the equivalent capacitance between points a and b. \((b)\) Determine the charge on each capacitor and the potential difference across each in terms of \(V\). Equation Transcription: Text Transcription: C_1=C_2=C_3=C_4=C C_1 C_2 C_3 C_4

Estimate the value of resistances needed to make a variable timer for intermittent windshield wipers: one wipe every 15 s, 8 s, 4 s, 2 s, 1 s. Assume the capacitor used is on the order of \(1~ \mathrm \mu F\). See Fig. 19–67.

Electrocardiographs are often connected as shown in Fig. 19–68. The lead wires to the legs are said to be capacitively coupled. A time constant of 3.0 s is typical and allows rapid changes in potential to be recorded accurately. If \(C=3.0~ \mu \mathrm F\), what value must \(R\) have? [\(Hint\): Consider each leg as a separate circuit.] ________________ Equation Transcription: Text Transcription: C=3.0 muF

In Fig. 19–69 (same as Fig. 19–20a), the total resistance is 15.0 k\(\Omega\) and the battery’s emf is 24.0 V. If the time constant is measured to be 18.0 \(\mu\)s calculate \((a)\) the total capacitance of the circuit and \((b)\) the time it takes for the voltage across the resistor to reach 16.0 V after the switch is closed. ________________ Equation Transcription: Text Transcription: 18.0 mu s 15.0 k Omega

(II) Two 3.8-\(\mu\)F capacitors, two 2.2-k\(\Omega\) resistors, and a 16.0-V source are connected in series. Starting from the uncharged state, how long does it take for the current to drop from its initial value to 1.50 mA? Equation Transcription: Text Transcription:

The \(RC\) circuit of Fig. 19–70 (same as Fig. 19–21a) has \(R=8.7~ \mathrm k \Omega\) and \(C=3.0~ \mu \mathrm F\). The capacitor is at voltage \(V_0\) at \(t=0\), when the switch is closed. How long does it take the capacitor to discharge to 0.25% of its initial voltage? ________________ Equation Transcription: Text Transcription: R=8.7 k Omega C=3.0 mu F V_0 t=0

Consider the circuit shown in Fig. 19–71, where all resistors have the same resistance \(R\). At \(t=0\), with the capacitor \(C\) uncharged, the switch is closed. \((a)\) At \(t=0\), the three currents can be determined by analyzing a simpler, but equivalent, circuit. Draw this simpler circuit and use it to find the values of \(I_1\), \(I_2\), and \(I_3\) at \(t=0\). \((b)\) At \(t=\infty\), the currents can be determined by analyzing a simpler, equivalent circuit. Draw this simpler circuit and implement it in finding the values of \(I_1\), \(I_2\), and \(I_3\) at \(t=\infty\). (\((c)\) At \(t=\infty\), what is the potential difference across the capacitor? Equation Transcription: Text Transcription: t=0 t=0 I_1 I_2 I_3 t=0 t=infty I_1 I_2 I_3 t=infty t=infty

Two resistors and two uncharged capacitors are arranged as shown in Fig. 19–72. Then a potential difference of 24 V is applied across the combination as shown. \((a)\) What is the potential at point a with switch S open? (Let \(V=0\) at the negative terminal of the source.) \((b)\) What is the potential at point b with the switch open? \((c)\) When the switch is closed, what is the final potential of point b? \((d)\) How much charge flows through the switch S after it is closed? Equation Transcription: Text Transcription: V=0 8.8 Omega 4.4 Omega 0.48 mu F 0.36 mu F

\((a)\) An ammeter has a sensitivity of 35,000 \(\Omega\)/V. What current in the galvanometer produces full-scale deflection? \((b)\) What is the resistance of a voltmeter on the 250-V scale if the meter sensitivity is 35,000 \(\Omega\)/V? Equation Transcription: Text Transcription: 35,000 Omega/V 35,000 Omega/V

(II) An ammeter whose internal resistance is 53 \(\Omega\) reads 5.25 mA when connected in a circuit containing a battery and two resistors in series whose values are 720 \(\Omega\) and 480 \(\Omega\). What is the actual current when the ammeter is absent? Equation Transcription: Text Transcription: 53 Omega 720 Omega 480 Omega

(II) A milliammeter reads 35 mA full scale. It consists of a 0.20-\(\Omega\) resistor in parallel with a 33-\(\Omega\) galvanometer. How can you change this ammeter to a voltmeter giving a full-scale reading of 25 V without taking the ammeter apart? What will be the sensitivity (\(\Omega\)/V) of your voltmeter? Equation Transcription: Text Transcription: 0.20-Omega 33-Omega (Omega/V)

(II) A galvanometer has an internal resistance of 32 \(\Omega\) and deflects full scale for a 55-\(\mu\)A current. Describe how to use this galvanometer to make \((a)\) an ammeter to read currents up to 25 A, and \((b)\) a voltmeter to give a full-scale deflection of 250 V. Equation Transcription: Text Transcription: 32 Omega 55-mu A

(III) A battery with \(\mathscr{E} = 12.0\ V\) and internal resistance \(r = 1.0\ \Omega\) is connected to two \(7.5-k\Omega\) resistors in series. An ammeter of internal resistance \(0.50\ \Omega\) measures the current, and at the same time a voltmeter across one of the \(7.5-k\Omega\) resistors in the circuit. What do the ammeter and voltmeter read? What is the %“error” from the current and voltage without meters?

(III) What internal resistance should the voltmeter of Example 19–17 have to be in error by less than 5%?

(III) Two 9.4-k\(\Omega\) resistors are placed in series and connected to a battery. A voltmeter of sensitivity 1000 \(\Omega\)/V is on the 3.0-V scale and reads 1.9 V when placed across either resistor. What is the emf of the battery? (Ignore its internal resistance.) Equation Transcription: Text Transcription: 9.4-k Omega 1000 Omega/V

When the resistor R in Fig. 19–73 is 35 \(\Omega\), the high- resistance voltmeter reads 9.7 V. When \(R\) is replaced by a 14.0-\(\Omega\) resistor, the voltmeter reading drops to 8.1 V. What are the emf and internal resistance of the battery? Equation Transcription: Text Transcription: 35 Omega 14.0-Omega

Suppose that you wish to apply a 0.25-V potential difference between two points on the human body. The resistance is about 1800 \(\Omega\), and you only have a 1.5-V battery. How can you connect up one or more resistors to produce the desired voltage? Equation Transcription: Text Transcription: 1800 Omega

A three-way lightbulb can produce 50 W, 100 W, or 150 W, at 120 V. Such a bulb contains two filaments that can be connected to the 120 V individually or in parallel (Fig. 19–74). \((a)\) Describe how the connections to the two filaments are made to give each of the three wattages. \((b)\) What must be the resistance of each filament?"

What are the values of effective capacitance which can be obtained by connecting four identical capacitors, each having a capacitance C?

Electricity can be a hazard in hospitals, particularly to patients who are connected to electrodes, such as an ECG. Suppose that the motor of a motorized bed shorts out to the bed frame, and the bed frame’s connection to a ground has broken (or was not there in the first place). If a nurse touches the bed and the patient at the same time, the nurse becomes a conductor and a complete circuit can be made through the patient to ground through the ECG apparatus. This is shown schematically in Fig. 19–75. Calculate the current through the patient. Equation Transcription: Text Transcription: 10^4 Omega 10^4 Omega 10^4 Omega

A heart pacemaker is designed to operate at using a capacitor in a simple RC circuit. What value of resistance should be used if the pacemaker is to fire (capacitor discharge) when the voltage reaches 75% of maximum and then drops to 0 V (72 times a minute)?

Suppose that a person’s body resistance is 950 \(\Omega\) (moist skin). \((a)\) What current passes through the body when the person accidentally is connected to 120 V? \((b)\) If there is an alternative path to ground whose resistance is 25 \(\Omega\), what then is the current through the body? \((c)\) If the voltage source can produce at most 1.5 A, how much current passes through the person in case \((b)\)? Equation Transcription: Text Transcription: 950 Omega 25 Omega

One way a multiple-speed ventilation fan for a car can be designed is to put resistors in series with the fan motor. The resistors reduce the current through the motor and make it run more slowly. Suppose the current in the motor is 5.0 A when it is connected directly across a 12-V battery. (a) What series resistor should be used to reduce the current to 2.0 A for low-speed operation? (b) What power rating should the resistor have? Assume that the motors resistance is roughly the same at all speeds.

A Wheatstone bridge is a type of “bridge circuit” used to make measurements of resistance. The unknown resistance to be measured, \(R_x\), is placed in the circuit with accurately known resistances \(R_1\), \(R_2\), and \(R_3\) (Fig. 19–76). One of these, \(R_3\), is a variable resistor which is adjusted so that when the switch is closed momentarily, the ammeter ? shows zero current flow. The bridge is then said to be balanced. \((a)\) Determine \(R_x\) in terms of \(R_1\), \(R_2\), and \(R_3\). \((b)\) If a Wheatstone bridge is “balanced” when \(R_1=590~ \Omega\), \(R_2=972~ \Omega\), and \(R_3=78.6~ \Omega\), what is the value of the unknown resistance? Equation Transcription: Text Transcription: R_x R_1 R_2 R_3 R_3 R_x R_1 R_2 R_3 R_1=590 Omega R_2=972 Omega R_3=78.6 Omega I_3 R_3 R_x I_1 R_1 R_2

The internal resistance of a 1.35-V mercury cell is 0.030 \(\Omega\), whereas that of a 1.5-V dry cell is 0.35 \(\Omega\). Explain why three mercury cells can more effectively power a 2.5-W hearing aid that requires 4.0 V than can three dry cells. Equation Transcription: Text Transcription: 0.030 Omega 0.035 Omega

How many \(\frac{1}{2}\)-W resistors, each of the same resistance, must be used to produce an equivalent 3.2-k\(\Omega\), 3.5-W resistor? What is the resistance of each, and how must they be connected? Do not exceed \(P=\frac{1}{2} \mathrm W\) in each resistor. Equation Transcription: Text Transcription: frac{1}{2} 3.2-k Omega P=frac{1}{2}W

A solar cell, 3.0 cm square, has an output of 350 mA at 0.80 V when exposed to full sunlight. A solar panel that delivers close to 1.3 A of current at an emf of 120 V to an external load is needed. How many cells will you need to create the panel? How big a panel will you need, and how should you connect the cells to one another?

The current through the 4.0-k\(\Omega\) resistor in Fig. 19–77 is 3.10 mA. What is the terminal voltage \(V_\mathrm{ba}\) of the “unknown” battery? (There are two answers. Why?) ________________ Equation Transcription: Text Transcription: 4.0-k Omega V_ba V_ba V_ba 3.2 k Omega 1.0 k Omega 8.0 k Omega 4.0 k Omega

A power supply has a fixed output voltage of 12.0 V, but you need \(V_\mathrm{T}=3.5~ \mathrm V\) output for an experiment. \((a)\) Using the voltage divider shown in Fig. 19–78, what should \(R_2\) be if \(R_1\) is 14.5 \(\Omega\)? \((b)\) What will the terminal voltage \(V_\mathrm{T}\) be if you connect a load to the 3.5-V output, assuming the load has a resistance of 7.0 \(\Omega\)? Equation Transcription: Text Transcription: V_T=3.5 V R_2 R_1 14.5 Omega V_T 7.0 Omega R_1 R_2 V_T

A battery produces 40.8 V when 8.40 A is drawn from it, and 47.3 V when 2.80 A is drawn. What are the emf and internal resistance of the battery?

In the circuit shown in Fig. 19–79, the 33-\(\Omega\) resistor dissipates 0.80 W. What is the battery voltage? ________________ Equation Transcription: Text Transcription: 33-Omega 33 Omega 68 Omega 85 Omega

For the circuit shown in Fig. 19–80, determine \((a)\) the current through the 16-V battery and \((b)\) the potential difference between points a and b, \(V_\mathrm a-V_\mathrm b\). ________________ Equation Transcription: Text Transcription: V_a-V_b 10 k Omega 13 k Omega 12 k Omega 18 k Omega

The current through the 20-\(\Omega\) resistor in Fig. 19–81 does not change whether the two switches \(S_1\) and \(S_2\) are both open or both closed. Use this clue to determine the value of the unknown resistance \(R\). ________________ Equation Transcription: Text Transcription: S_1 S_2 20 Omega 50 Omega 10 Omega S_1 S_2

\((a)\) What is the equivalent resistance of the circuit shown in Fig. 19–82? [\(Hint\): Redraw the circuit to see series and parallel better.] \((b)\) What is the current in the 14-\(\Omega\) resistor? \((c)\) What is the current in the 12-\(\Omega\) resistor? \((d)\) What is the power dissipation in the 4.5-\(\Omega\) resistor? ________________ Equation Transcription: Text Transcription: 14-Omega 12-Omega 4.5-Omega 12 Omega 22 Omega 14 Omega 4.5 Omega

A voltmeter and an ammeter can be connected as shown in Fig. 19–83a to measure a resistance \(R\). If \(V\) is the voltmeter reading, and I is the ammeter reading, the value of \(R\) will not quite be \(V/I\) (as in Ohm’s law) because some current goes through the voltmeter. Show that the actual value of \(R\) is \(\frac{1}{R}=\frac{I}{V}-\frac{1}{R_\mathrm V}\), where \(R_\mathrm V\) is the voltmeter resistance. Note that \(R~{\approx}~V/I \) if \(R_\mathrm V \gg R\). \((b)\) A voltmeter and an ammeter can also be connected as shown in Fig. 19–83b to measure a resistance \(R\). Show in this case that \(R=\frac{V}{I}-R_\mathrm A\), where \(V\) and \(I\) are the voltmeter and ammeter readings and \(R_\mathrm A\) is the resistance of the ammeter. Note that \(R~{\approx}~V/I \) if \(R_\mathrm A \ll R\). ________________ Equation Transcription: Text Transcription: frac{1}{R}=frac{I}{V}-frac{1}{R_V} R_V R{approx}V/I R_V >> R R=frac{V}{I}-R_A R{approx}V/I R_A << R

The circuit shown in Fig. 19–84 uses a neon-filled tube as in Fig. 19–23a. This neon lamp has a threshold voltage \(V_0\) for conduction, because no current flows until the neon gas in the tube is ionized by a sufficiently strong electric field. Once the threshold voltage is exceeded, the lamp has negligible resistance. The capacitor stores electrical energy, which can be released to flash the lamp. Assume that \(C=0.150~ \mu \mathrm F\), \(R=2.35 \times 10^6~ \Omega\), \(V_0=90.0~\mathrm V\), and \(\varepsilon=105 V\). \((a)\) Assuming the circuit is hooked up to the emf at time \(t=0\), at what time will the light first flash? \((b)\) If the value of \(R\) is increased, will the time you found in part \((a)\) increase or decrease? \((c)\) The flashing of the lamp is very brief. Why? \((d)\) Explain what happens after the lamp flashes for the first time. Equation Transcription: Text Transcription: V_0 C=0.150 muF R=2.35 x 10^6 Omega V_0=90.0 V E=105 V t=0 E=105 V

A flashlight bulb rated at 2.0 W and 3.0 V is operated by a 9.0-V battery. To light the bulb at its rated voltage and power, a resistor \(R\) is connected in series as shown in Fig. 19–85. What value should the resistor have?

In Fig. 19–86, let \(V=10.0~ \mathrm V\) and \(C_1=C_2=C_3=25.4~ \mu \mathrm F\). How much energy is stored in the capacitor network \((a)\) as shown, \((b)\) if the capacitors were all in series, and \((c)\) if the capacitors were all in parallel? ________________ Equation Transcription: Text Transcription: V=10.0 V C_1=C_2=C_3=25.4 muF C_1 C_2 C_3

A 12.0-V battery, two resistors, and two capacitors are connected as shown in Fig. 19–87. After the circuit has been connected for a long time, what is the charge on each capacitor? ________________ Equation Transcription: Text Transcription: 1.3 k Omega 1.3 k Omega 12 mu F 48 mu F

Determine the current in each resistor of the circuit shown in Fig. 19–88. ________________ Equation Transcription: Text Transcription: 5.00 Omega 6.00 Omega 12.00 Omega 6.80 Omega

How much energy must a 24-V battery expend to charge a 0.45-\(\mu\)F and a 0.20-\(\mu\)F capacitor fully when they are placed \((a)\) in parallel, \((b)\) in series? \((c)\) How much charge flowed from the battery in each case? Equation Transcription: Text Transcription: 0.45-mu F 0.20-mu F

Two capacitors, \(C_1=2.2~ \mu \mathrm F\) and \(C_2=1.2~ \mu \mathrm F\), are connected in parallel to a 24-V source as shown in Fig. 19–89a. After they are charged they are disconnected from the source and from each other, and then reconnected directly to each other with plates of opposite sign connected together (see Fig. 19–89b). Find the charge on each capacitor and the potential across each after equilibrium is established (Fig. 19–89c). Equation Transcription: Text Transcription: C_1=2.2 mu F C_2=1.2 mu F C_1 +Q_1 +Q_2 -Q_1 -Q_2 C_1 C_2 +Q_1 -Q_2 -Q_1 +Q_2

The switch S in Fig. 19–90 is connected downward so that capacitor \(C_2\) becomes fully charged by the battery of voltage \(V_0\). If the switch is then connected upward, determine the charge on each capacitor after the switching. Equation Transcription: Text Transcription: C_2 V_0

The performance of the starter circuit in a car can be significantly degraded by a small amount of corrosion on a battery terminal. Figure 19–91a depicts a properly functioning circuit with a battery (12.5-V emf, 0.02-\(\Omega\) internal resistance) attached via corrosion-free cables to a starter motor of resistance \(R_\mathrm S=0.15~\Omega\). Sometime later, corrosion between a battery terminal and a starter cable introduces an extra series resistance of only \(R_\mathrm C=0.10~\Omega\) into the circuit as suggested in Fig. 19–91b. Let \(P_0\) be the power delivered to the starter in the circuit free of corrosion, and let \(P\) be the power delivered to the circuit with corrosion. Determine the ratio \(P/P_0\) Equation Transcription: Text Transcription: 0.02-Omega R_s=0.15 Omega R_C=0.10 Omega P_0 P/P_0 E=12.5 V r=0.02 Omega R_S=0.15 Omega R_C=0.10 Omega E=12.5 V r=0.02 Omega R_S=0.15 Omega

The variable capacitance of an old radio tuner consists of four plates connected together placed alternately between four other plates, also connected together (Fig. 19–92). Each plate is separated from its neighbor by 1.6 mm of air. One set of plates can move so that the area of overlap of each plate varies from \(2.0~ \mathrm {cm^2}\) to \(9.0~ \mathrm {cm^2}\). \((a)\) Are these seven capacitors connected in series or in parallel? \((b)\) Determine the range of capacitance values. ________________ Equation Transcription: Text Transcription: 2.0 cm^2 9.0 cm^2

A 175-pF capacitor is connected in series with an unknown capacitor, and as a series combination they are connected to a 25.0-V battery. If the 175-pF capacitor stores 125 pC of charge on its plates, what is the unknown capacitance?

In the circuit shown in Fig. 19–93, \(C_1 = 1.0\ \mu F\), \(C_2 = 2.0\ \mu F\), \(C_3 = 2.4\ \mu F\), and a voltage \(V_{ab} = 24\ V\) is applied across points a and b. After \(C_1\) is fully charged, the switch is thrown to the right. What is the final charge and potential difference on each capacitor?

The automobile headlight bulbs shown in the circuits here are identical. The battery connection which produces more light is (a) circuit 1. (b) circuit 2. (c) both the same. (d) not enough information

In which circuits shown in Fig. 19-40 are resistors connected in series?

Problem 1P (I) Calculate the terminal voltage for a battery with an internal resistance of 0.900? and an emf of 6.00 V when the battery is connected in series with (a) a 71.0- ? resistor, and (b) a 71.0- ? resistor.

Problem 1Q Explain why birds can sit on power lines safely, even though the wires have no insulation around them, whereas leaning a metal ladder up against a power line is extremely dangerous.

Compare the formulas for resistors and for capacitors when connected in series and in parallel by filling in the Table below. Discuss and explain the differences. Consider the role of voltage V.

Which resistors in Fig. 19–41 are connected in parallel? (a) All three. (b) \(R_{1}\) and \(R_{2}\). (c) \(R_{2}\) and \(R_{3}\). (d) \(R_{1}\) and \(R_{3}\) ( ) None of the above. Equation transcription: Text transcription: R{1} R{2} R{3}

Problem 2P (I) Four 1.50-V cells are connected in series to a 12.0-? lightbulb. If the resulting current is 0.45 A, what is the internal resistance of each cell, assuming they are identical and neglecting the resistance of the wires?

Problem 2Q Discuss the advantages and disadvantages of Christmas tree lights connected in parallel versus those connected in series.

Problem 2SL Fill in the Table below for a combination of two unequal resistors of resistance R1 and R2 Assume the electric potential on the low-voltage end of the combination is VA volts and the potential at the high-voltage end of the combination is VB volts. First draw diagrams. Property Resistors in Series Resistors in parallel Equivalent resistance Current through equivalent resistance Voltage across equivalent resistance Voltage across the pair of resistors Voltage across each resistor V 1= V2 = V1 = V2 = Voltage at a point between the resistors Not applicable Current through each resistor I1 = I2 = I1 = I2 =

Problem 3MCQ A resistor 10,000- ? is placed in series with a 100 – ? resistor. The current in the 10,000 – ? resistor is 10 A. If the resistors are swapped, how much current flows through the 100 - ? resistor? (a) > 10 A. (b) < 10 A. (c) 10 A. (d) Need more information about the circuit.

Problem 3P (II) What is the internal resistance of a 12.0-V car battery whose terminal voltage drops to 8.8 V when the starter motor draws 95 A? What is the resistance of the starter?

Problem 3Q If all you have is a 120-V line, would it be possible to light several 6-V lamps without burning them out? How?

Problem 3SL Cardiac defibrillators are discussed in Section 17–9. (a) Choose a value for the resistance so that 1.0 - ?F the capacitor can be charged to 3000 V in 2.0 seconds. Assume that this 3000 V is 95%of the full source voltage. (b) The effective resistance of the human body is given in Section 19–7. If the defibrillator discharges with a time constant of 10 ms, what is the effective capacitance of the human body?

Two identical batteries and two identical \(10-\Omega\) resistors are placed in series as shown in Fig. 19-42. If a \(10-\Omega\) lightbulb is connected with one end connected between the batteries and other end between the resistors, how much current will flow through the lightbulb? (a) . (b) . (c) . Equation transcription: Text transcription: 10-Omega

Problem 4P (I) A 650-? and an 1800--? resistor are connected in series with a 12-V battery. What is the voltage across the 1800-? resistor?

Problem 4Q Two lightbulbs of resistance \(R_{1}\) and \(R_{2}\left(R_{2}>R_{1}\right)\) and a battery are all connected in series. Which bulb is brighter? What if they are connected in parallel? Explain. Equation Transcription: Text Transcription: R_1 R_2 (R_2 > R_1)

A potentiometer is a device to precisely measure potential differences or emf, using a null technique. In the simple potentiometer circuit shown in Fig. represents the total resistance of the resistor from to (which could be a long uniform "slide" wire), whereas represents the resistance of only the part from A to the movable contact at . When the unknown emf to be measured, \(E_{x}\), is placed into the circuit as shown, the movable contact is moved until the galvanometer G gives a null reading (i.e., zero) when the switch is closed. The resistance between and for this situation we call \(R_{x}\) Next, a standard emf, \(E_{s}\), which is known precisely, is inserted into the circuit in place of \(E_{x}\) and again the contact is moved until zero current flows through the galvanometer when the switch is closed. The resistance between and now is called \(R_{s}\) Show that the unknown emf is given by \(E_{x}=\left(\frac{R_{x}}{R_{x}}\right) E_{s}\) where , and are all precisely known. The working battery is assumed to be fresh and to give a constant voltage. Equation transcription: Text transcription: E{s} E{x} R{s} E{x}=(frac{R{x}}{R{x}}) E{s} R{x}

Which resistor shown in Fig. 19-43 has the greatest current going through it? Assume that all the resistors are equal. (a) \(R_{1}\). (b) \(R_{1} \text { and } R_{2}\). (c) \(R_{3} \text { and } R_{4}\). (d) \(R_{5}\). (e) All of them the same. Equation Transcription: Text Transcription: R_1 R_1 and R_2 R_3 and R_4 R_5

Problem 5P (I) Three 45-? light bulbs and three 65--? lightbulbs are connected in series. (a) What is the total resistance of the circuit? (b) What is the total resistance if all six are wired in parallel?

Problem 5Q Household outlets are often double outlets. Are these connected in series or parallel? How do you know?

The circuit shown in Fig. 19-95 is a primitive 4-bit digital to-analog converter . In this circuit, to represent each digit \(\left(2^{n}\right)\) of a binary number, a "1" has the \(n^{t h}) switch closed whereas zero ("0") has the switch open. For example, 0010 is represented by closing switch , while all other switches are open. Show that the voltage across the \(1.0 \Omega\) resistor for the binary numbers 0001,0010 , 0100 , and 1001 (which in decimal represent follows the pattern that you expect for a 4-bit DAC. (Section 17-10 may help.) Equation transcription: Text transcription: (2^{n}) n^{t h} 1.0 Omega

Figure 19–44 shows three identical bulbs in a circuit. What happens to the brightness of bulb A if you replace bulb B with a short circuit? () Bulb A gets brighter. (b ) Bulb A gets dimmer. (c ) Bulb A’s brightness does not change. (d ) Bulb A goes out.

Problem 6P (II) Suppose that you have a 580-?, a 790- ?, and a 1.20 -k ? resistor. What is (a) the maximum, and (b) the minimum resistance you can obtain by combining these?

Problem 6Q With two identical light bulbs and two identical batteries, explain how and why you would arrange the bulbs and batteries in a circuit to get the maximum possible total power to the light bulbs. (Ignore internal resistance of batteries.)

When the switch shown in Fig. 19–45 is closed, what will happen to the voltage across resistor \(R_{4}\). It will () increase. (b) decrease. (c) stay the same. Equation transcription: Text transcription: R{4}

Problem 7P (II) How many 10-? resistors must be connected in series to give an equivalent resistance to five 100- ? resistors connected in parallel?

Problem 7Q If two identical resistors are connected in series to a battery, does the battery have to supply more power or less power than when only one of the resistors is connected? Explain.

When the switch shown in Fig. 19–45 is closed, what will happen to the voltage across resistor \(R_{1}\)? It will (a) increase. (b) decrease. (c) stay the same. Equation Transcription: Text Transcription: R_1

II) Design a “voltage divider” (see Example 19–3) that would provide one-fifth (0.20) of the battery voltage across \(R_{2}\), Fig.19-6. What is the ratio \(R_{1} / R_{2}\)? Equation transcription: Text transcription: R{2} R{1} / R{2}

Problem 8Q You have a single 60-W bulb lit in your room. How does the overall resistance of your room’s electric circuit change when you turn on an additional 100-W bulb? Explain.

Problem 9MCQ As a capacitor is being charged in an RC circuit, the current flowing through the resistor is (a) increasing. (c) constant. (b) decreasing. (d) zero.

Problem 9P (II) Suppose that you have a 9.0-V battery and wish to apply a voltage of only 3.5 V. Given an unlimited supply of 1.0-? resistors, how could you connect them to make a “voltage divider” that produces a 3.5-V output for a 9.0-V input?

Problem 9Q Suppose three identical capacitors are connected to a battery. Will they store more energy if connected in series or in parallel?

For the circuit shown in Fig. 19–46, what happens when the switch S is closed? (a) Nothing. Current cannot flow through the capacitor. (b) The capacitor immediately charges up to the battery emf. (c) The capacitor eventually charges up to the full battery emf at a rate determined by R and C. (d) The capacitor charges up to a fraction of the battery emf determined by R and C. (e) The capacitor charges up to a fraction of the battery emf determined by R only.

(II) Three \(1.70-k\Omega\) resistors can be connected together in four different ways, making combinations of series and/or parallel circuits. What are these four ways, and what is the net resistance in each case?

When applying Kirchhoff’s loop rule (such as in Fig. 19–36), does the sign (or direction) of a battery’s emf depend on the direction of current through the battery? What about the terminal voltage?

The capacitor in the circuit shown in Fig. 19-47 is charged to an initial value Q. When the switch is closed, it discharges through the resistor. It takes 2.0 seconds for the charge to drop to \(\frac{1}{2} Q\). How long does it take to drop to \(\frac{1}{4} Q\)? (a) 3.0 seconds. (b) 4.0 seconds. (c) Between 2.0 and 3.0 seconds. (d) Between 3.0 and 4.0 seconds. (e) More than 4.0 seconds. Equation Transcription: Text Transcription: 1/2Q 1/4Q

(II) A battery with an emf of 12.0V shows a terminal voltage of 11.8 V when operating in a circuit with two lightbulbs each rated at 4.0 W (at 12.0 V), which are connected in parallel. What is the battery's internal resistance?

Different lamps might have batteries connected in either of the two arrangements shown in Fig. 19–37. What would be the advantages of each scheme?

Problem 12MCQ A resistor and a capacitor are used in series to control the timing in the circuit of a heart pacemaker. To design a pacemaker that can double the heart rate when the patient is exercising, which statement below is true? The capacitor (a) needs to discharge faster, so the resistance should be decreased. (b) needs to discharge faster, so the resistance should be increased. (c) needs to discharge slower, so the resistance should be decreased. (d) needs to discharge slower, so the resistance should be increased. (e) does not affect the timing, regardless of the resistance.

Problem 12P (II) Eight identical bulbs are connected in series across a 120-V line. (a) What is the voltage across each bulb? (b) If the current is 0.45 A, what is the resistance of each bulb, and what is the power dissipated in each?

For what use are batteries connected in series? For what use are they connected in parallel? Does it matter if the batteries are nearly identical or not in either case?

Problem 13MCQ Why is an appliance cord with a three-prong plug safer than one with two prongs? (a) The 120 V from the outlet is split among three wires, so it isn’t as high a voltage as when it is only split between two wires. (b) Three prongs fasten more securely to the wall outlet. (c) The third prong grounds the case, so the case cannot reach a high voltage. (d) The third prong acts as a ground wire, so the electrons have an easier time leaving the appliance. As a result, fewer electrons build up in the appliance. (e) The third prong controls the capacitance of the appliance, so it can’t build up a high voltage.

Problem 13P (II) Eight bulbs are connected in parallel to a 120-V source by two long leads of total resistance 1.4 ? If 210 mA flows through each bulb, what is the resistance of each, and what fraction of the total power is wasted in the leads?

Problem 13Q Can the terminal voltage of a battery ever exceed its emf? Explain.

Problem 14MCQ When capacitors are connected in series, the effective capacitance is __________ the smallest capacitance; when capacitors are connected in parallel, the effective capacitance is __________ the largest capacitance. (a) greater than; equal to. (d) equal to; less than. (b) greater than; less than. (e) equal to; equal to. (c) less than; greater than.

Problem 14P (II) A close inspection of an electric circuit reveals that a 480-? resistor was inadvertently soldered in the place where a 350- ? resistor is needed. How can this be fixed without removing anything from the existing circuit?

Explain in detail how you could measure the internal resistance of a battery.

Problem 15MCQ If ammeters and voltmeters are not to significantly alter the quantities they are measuring, (a) the resistance of an ammeter and a voltmeter should be much higher than that of the circuit element being measured. (b) the resistance of an ammeter should be much lower, and the resistance of a voltmeter should be much higher, than those of the circuit being measured. (c) the resistance of an ammeter should be much higher, and the resistance of a voltmeter should be much lower, than those of the circuit being measured. (d) the resistance of an ammeter and a voltmeter should be much lower than that of the circuit being measured. (e) None of the above.

Problem 15P (II) Eight 7.0-W Christmas tree lights are connected in series to each other and to a 120-V source. What is the resistance of each bulb?

Problem 15Q In an RC circuit, current flows from the battery until the capacitor is completely charged. Is the total energy supplied by the battery equal to the total energy stored by the capacitor? If not, where does the extra energy go?

(II) Determine () the equivalent resistance of the circuit shown in Fig. 19–48, (b) the voltage across each resistor, and (c) the current through each resistor.

Given the circuit shown in Fig. 19-38, use the words "increases," "decreases," or "stays the same" to complete the following statements: () If \(R_{7}\) increases, the potential difference between and ___________________. Assume no resistance in and . (b) If \(R_{7}\) increases, the potential difference between and ___________________. Assume and \(\varepsilon\) have resistance. (c) If R7 increases, the voltage drop across \(R_{4}\) __________________. (d) If R2 decreases, the current through \(R_{1}\)__________________. (e) If R2 decreases, the current through \(R_{6}\)__________________. (f) If R2 decreases, the current through \(R_{3}\)_________________. (g) If R5 increases, the voltage drop across \(R_{2}\)________________. (h) If R5 increases, the voltage drop across \(R_{4}\)________________. (i) If \(R_{2^{\prime}} R_{5}\), and \(R_{7}\) increase, \(\varepsilon(r=0)\) ______________________. Figure 19-38 Question 16, \(R_{2^{\prime}} R_{5}\) and \(R_{7}\) are variable resistors (you can change their resistance), given the symbol Equation transcription: Text transcription: R_{7} \varepsilon R_{1} R_{6} R_{3} R_{2} R_{4} R_{2^{\prime}} R_{5} R_{7} \varepsilon(r=0)

Problem 17P (II) A 75-W, 120-V bulb is connected in parallel with a 25-W, 120-V bulb. What is the net resistance?

Design a circuit in which two different switches of the type shown in Fig. 19–39 can be used to operate the same lightbulb from opposite sides of a room.

(II) () Determine the equivalent resistance of the “ladder” of equal \(175-\Omega\) resistors shown in Fig. 19–49. In other words, what resistance would an ohmmeter read if connected between points A and B? (b) What is the current through each of the three resistors on the left if a 50.0-V battery is connected between points A and B? Equation transcription: Text transcription: 175-Omega

Problem 18Q Why is it more dangerous to turn on an electric appliance when you are standing outside in bare feet than when you are inside wearing shoes with thick soles?

Return to the Chapter-Opening Question, page 526, and answer it again now. Try to explain why you may have answered differently the first time.

You have a \(10-\Omega\) and a \(15-\Omega\) resistor. What is the smallest and largest equivalent resistance that you can make with these two resistors? Equation transcription: Text transcription: 10-Omega 15-Omega

A 100-W, 120-V lightbulb and a 60-W, 120-V lightbulb are connected in two different ways as shown in Fig. 19–9. In each case, which bulb glows more brightly? Ignore change of filament resistance with current (and temperature).

Write the Kirchhoff equation for the lower loop abcdefga of Example 19–8 and show, assuming the currents calculated in this Example, that the potentials add to zero for this lower loop.

If the jumper cables of Example 19–9 were mistakenly connected in reverse, the positive terminal of each battery would be connected to the negative terminal of the other battery (Fig. 19–16). What would be the current I even before the starter motor is engaged (the switch S in Fig. 19–16 is open)? Why could this cause the batteries to explode?

Consider two identical capacitors What are the smallest and largest capacitances that can be obtained by connecting these in series or parallel combinations? () \(0.2 \mu F, 5 \mu F\) (b) \(0.2 \mu F, 10 \mu F\) (c) \(0.2 \mu F, 20 \mu F\)(d) \(5 \mu F, 10 \mu F\) (e) \(5 \mu F, 20 \mu F\) (f) \(10 \mu F, 20 \mu F\) Equation transcription: Text transcription: 0.2 \mu F, 5 \mu F 0.2 \mu F, 10 \mu F 0.2 \mu F, 20 \mu F 5 \mu F, 10 \mu F 5 \mu F, 20 \mu F 10 \mu F, 20 \mu F

Problem 19EG A typical turn signal flashes perhaps twice per second, so it's time constants on the order of 0.5 s. Estimate the resistance in the circuit, assuming a moderate capacitor of C = 1?F.

(II) What is the net resistance of the circuit connected to the battery in Fig. 19–50?

Problem 19Q What is the main difference between an analog voltmeter and an analog ammeter?

Problem 20P (II) Calculate the current through each resistor in Fig. 19–50 if each resistance R =3.25 k? and V =12.0 V. What is the potential difference between points A and B?

Problem 20Q What would happen if you mistakenly used an ammeter where you needed to use a voltmeter?

Problem 21P (III) Two resistors when connected in series to a 120-V line use one-fourth the power that is used when they are connected in parallel. If one resistor is 4.8 k ?, what is the resistance of the other?

Problem 21Q Explain why an ideal ammeter would have zero resistance and an ideal voltmeter infinite resistance.

(III) Three equal resistors (R) are connected to a battery as shown in Fig. 19–51. Qualitatively, what happens to () the voltage drop across each of these resistors, (b) the current flow through each, and (c) the terminal voltage of the battery, when the switch S is opened, after having been closed for a long time? (d) If the emf of the battery is 9.0 V, what is its terminal voltage when the switch is closed if the internal resistance r is \(0.50 \Omega\) and \(R=5.50 \Omega\)? (e) What is the terminal voltage when the switch is open? Equation transcription: Text transcription: 0.50 Omega R=5.50 Omega

Problem 22Q A voltmeter connected across a resistor always reads less than the actual voltage (i.e., when the meter is not present). Explain.

Problem 23P (III) A and 2.5-k? a 3.7-k ? resistor are connected in parallel; this combination is connected in series with a 1.4-k ? resistor. If each resistor is rated at 0.5 W (maximum without overheating), what is the maximum voltage that can be applied across the whole network?

Problem 23Q A small battery-operated flashlight requires a single 1.5-V battery. The bulb is barely glowing. But when you take the battery out and check it with a digital voltmeter, it registers 1.5 V. How would you explain this?

(III) Consider the network of resistors shown in Fig. 19–52. Answer qualitatively: (a) What happens to the voltage across each resistor when the switch S is closed? (b) What happens to the current through each when the switch is closed? (c) What happens to the power output of the battery when the switch is closed? (d) Let \(R_{1}=R_{2}=R_{3}=R_{4}=155 \Omega\) and V = 22.0 V. Determine the current through each resistor before and after closing the switch. Are your qualitative predictions confirmed? Equation transcription: Text transcription: R{1}=R{2}=R{3}=R{4}=155 Omega

(I) Calculate the current in the circuit of Fig. 19–53, and show that the sum of all the voltage changes around the circuit is zero.

(II) Determine the terminal voltage of each battery in Fig. 19–54.

(II) Determine the magnitudes and directions of the currents in each resistor shown in Fig. 19-56. The batteries have emfs of \(\mathscr{E}_{1}=9.0 \mathrm{~V}\) and \(\mathscr{E}_{2}=12.0 \mathrm{~V}\) and the resistors have values of \(R_{1}=25 \Omega, R_{2}=68 \Omega, R_{1}\) and \(R_{3}=35 \Omega\) () Ignore internal resistance of the batteries. (b) Assume each battery has internal resistance \(r=1.0 \Omega\) Equation transcription: Text transcription: {E}{1}=9.0{~V} {E}{2}=12.0{~V} R{1}=25 Omega, R{2}=68 Omega, R{1} R{3}=35 Omega r=1.0 Omega

(II) For the circuit shown in Fig. 19–55, find the potential difference between points a and b. Each resistor has \(R=160 \Omega\) and each battery is 1.5 V. Equation transcription: Text transcription: R=160 Omega

(II) () What is the potential difference between points a and d in Fig. 19–57 (similar to Fig. 19–13, Example 19–8), and (b) what is the terminal voltage of each battery?

(II) Calculate the magnitude and direction of the currents in each resistor of Fig. 19–58.

(II) Determine the magnitudes and directions of the currents through \(R_{1}\) and \(R_{2}\) in Fig. 19 –59. Equation transcription: Text transcription: R{1} R{2}

Problem 32P (II) Repeat Problem 31, now assuming that each battery has an internal resistance r =1.4 ?

(III) () A network of five equal resistors R is connected to battery \(\mathscr{E}\) as shown in Fig. 19–60. Determine the current I that flows out of the battery. (b) Use the value determined for I to find the single resistor \(R_{e q}\) that is equivalent to the five-resistors network. Equation transcription: Text transcription: {E} R{e q}

(III) () Determine the currents \(I_{1}, I_{2}\), and \(I_{3}\) in Fig. 19–61. Assume the internal resistance of each battery is \(r=1.0 \Omega\). (b) What is the terminal voltage of the 6.0-V battery? Equation transcription: Text transcription: I{1}, I{2} I{3} r=1.0 Omega

(III) What would the current \(I_{1}\) be in Fig. 19–61 if the \(12-\Omega\) resistor is shorted out (resistance = 0)? Let \(r=1.0 \Omega\) Equation transcription: Text transcription: I{1} 12-Omega r=1.0 Omega

(II) Suppose two batteries, with unequal emfs of 2.00 V and 3.00 V, are connected as shown in Fig. 19–62. If each internal resistance is \(r=0.3509\), and \(R=4.00 \Omega\), what is the voltage across the resistor R? Equation transcription: Text transcription: r=0.3509 R=4.00 Omega

Problem 37P (II) A battery for a proposed electric car is to have three hundred 3-V lithium ion cells connected such that the total voltage across all of the cells is 300 V. Describe a possible connection configuration (using series and parallel connections) that would meet these battery specifications.

Problem 38P (I) (a) Six 4.8-µF capacitors are connected in parallel. What is the equivalent capacitance? (b) What is their equivalent capacitance if connected in series?

(I) A \(3.00-\mu F\) and a \(4.00-\mu F\) capacitor are connected in series, and this combination is connected in parallel with a \(2.00-\mu F\) capacitor (see Fig. 19–63). What is the net capacitance? Equation transcription: Text transcription: 3.00-mu F 4.00-mu F 2.00-mu F

(II) If 21.0 V is applied across the whole network of Fig. 19–63, calculate () the voltage across each capacitor and (b) the charge on each capacitor. \(C_{1}=3.00 \mu F\) \(C_{2}=4.00 \mu F\) \(C_{3}=2.00 \mu F\) \(V=21.0 \mathrm{~V}\) Equation transcription: Text transcription: C{1}=3.00 mu F C{2}=4.00 mu F C{3}=2.00 mu F V=21.0{~V}

Problem 41P (II) The capacitance of a portion of a circuit is to be reduced from 2900 pF to 1200 pF. What capacitance can be added to the circuit to produce this effect without removing existing circuit elements? Must any existing connections be broken to accomplish this?

Problem 42P (II) An electric circuit was accidentally constructed using A 7.0-µF capacitor instead of the required 16-µF value. Without removing the 7.0-µF capacitor, what can a technician add to correct this circuit?

Problem 43P (II) Consider three capacitors, of capacitance 3200 pF, 5800 pF, and 0.0100 µF. What maximum and minimum capacitance can you form from these? How do you make the connection in each case?

(II) Determine the equivalent capacitance between points a and b for the combination of capacitors shown in Fig. 19–64. \(C_{1}\) \(C_{2}\) \(C_{3}\) \(C_{4}\) Equation transcription: Text transcription: C{1} C{2} C{3} C{4}

(II) What is the ratio of the voltage \(V_{1}\) across capacitor \(c_{1}\) in Fig. 19–65 to the voltage \(V_{2}\) across capacitor \(C_{2}\)? \(C_{2}=1.0 \mu F\) \(C_{1}=1.0 \mu F\) \(C_{3}=1.0 \mu F\) Equation transcription: Text transcription: V{1} C{1} V{2} C{2} C{2}=1.0 mu F C{1}=1.0 mu F C{3}=1.0 mu F

Problem 46P (II) A 0.50-µF and a 1.4- µF capacitor are connected in series to a 9.0-V battery. Calculate (a) the potential difference across each capacitor and (b) the charge on each. (c) Repeat parts (a) and (b) assuming the two capacitors are in parallel.

Problem 47P (II) A circuit contains a single 250-pF capacitor hooked across a battery. It is desired to store four times as much energy in a combination of two capacitors by adding a single capacitor to this one. How would you hook it up, and what would its value be?

Problem 48P (II) Suppose three parallel-plate capacitors, whose plates have areas A1.A2, and A3 and separations d1,d2, and d3, are connected in parallel. Show, using only Eq. 17–8, that Eq. 19–5 is valid.

Problem 49P (II) Two capacitors connected in parallel produce an equivalent capacitance of 35.0 µF but when connected in series the equivalent capacitance is only 4.8 µF. What is the individual capacitance of each capacitor?

Problem 50P III) Given three capacitors, C1 =2.0 µF, C2 =1.5 µF, And C3 =3.0 µF, what arrangement of parallel and series connections with a 12-V battery will give the minimum voltage drop across the 2.0-µF capacitor? What is the minimum voltage drop?

(III) In Fig. 19–66, suppose \(C_{1}=C_{2}=C_{3}=C_{4}=C\). () Determine the equivalent capacitance between points a and b. (b) Determine the charge on each capacitor and the potential difference across each in terms of V. Equation transcription: Text transcription: C{1}=C{2}=C{3}=C{4}=C

(I) Estimate the value of resistances needed to make a variable timer for intermittent windshield wipers: one wipe every 15 s, 8 s, 4 s, 2 s, 1 s. Assume the capacitor used is on the order of \(1 \mu\) F. See Fig. 19 –67. Equation transcription: Text transcription: 1 \mu

(II) Electrocardiographs are often connected as shown in Fig. 19–68. The lead wires to the legs are said to be capacitively coupled. A time constant of 3.0 s is typical and allows rapid changes in potential to be recorded accurately. If \(C=3.0 \mu F\), what value must R have? [Hint: Consider each leg as a separate circuit.] Equation transcription: Text transcription: C=3.0 mu F

(II) In Fig. 19–69 (same as Fig. 19–20a), the total resistance is \(15.0\ k\Omega\), and the battery’s emf is 24.0 V. If the time constant is measured to be \(18.0\ \mu s\), calculate (a) the total capacitance of the circuit and (b) the time it takes for the voltage across the resistor to reach 16.0 V after the switch is closed.

Problem 55P (II) Two 3.8-µF capacitors, two 2.2-k? resistors, and a 16.0-V source are connected in series. Starting from the uncharged state, how long does it take for the current to drop from its initial value to 1.50 mA?

(II) The RC circuit of Fig. 19–70 (same as Fig. 19–21a) has \(R=8.7 k \Omega\) and \(C=3.0 \mu F\). The capacitor is at voltage \(V_{0}\) at t = 0, when the switch is closed. How long does it take the capacitor to discharge to 0.25% of its initial voltage? Equation transcription: Text transcription: R=8.7 k Omega C=3.0 mu F V{0}

(III) Consider the circuit shown in Fig. , where all resistors have the same resistance . At , with the capacitor uncharged, the switch is closed.() At , the three currents can be determined by analyzing a simpler, but equivalent, circuit. Draw this simpler circuit and use it to find the values of \(I_{1}, I_{2}\), and \(I_{3}\) at At \(t=\infty\), the currents can be determined by analyzing a simpler, equivalent circuit. Draw this simpler circuit and implement it in finding the values of \(I_{1}, I_{2}\), and \(I_{3}\) at \(t=\infty\)(c) At \(t=\infty\), what is the potential difference across the capacitor? Equation transcription: Text transcription: I{1}, I{2} I{3} t=infty

(III) Two resistors and two uncharged capacitors are arranged as shown in Fig. 19–72. Then a potential difference of 24 V is applied across the combination as shown. () What is the potential at point a with switch S open? (Let V= 0 at the negative terminal of the source.) (b) What is the potential at point b with the switch open? (c) When the switch is closed, what is the final potential of point b? (d) How much charge flows through the switch S after it is closed? \(8.8 \Omega\) \(4.4 \Omega\) \(0.48 \mu F\) \(0.36 \mu F\) Equation transcription: Text transcription: 8.8 Omega 4.4 Omega 0.48 mu F 0.36 mu F

Problem 59P (I) (a) An ammeter has a sensitivity of 35,000 ?/V. What current in the galvanometer produces full-scale deflection? (b) What is the resistance of a voltmeter on the 250-V scale if the meter sensitivity is 35,000 ?/V

Problem 60P (II) An ammeter whose internal resistance is 53 ? reads 5.25 mA when connected in a circuit containing a battery and two resistors in series whose values are 720 ? and 480 ?. What is the actual current when the ammeter is absent?

Problem 61P (II) A milliammeter reads 35 mA full scale. It consists of a 0.20-? resistor in parallel with a 33- ? galvanometer. How can you change this ammeter to a voltmeter giving a full-scale reading of 25 V without taking the ammeter apart? What will be the sensitivity (?/V) of your voltmeter?

Problem 62P (II) A galvanometer has an internal resistance of 32 ? and deflects full scale for a 55-µA current. Describe how to use this galvanometer to make (a) an ammeter to read currents up to 25 A, and (b) a voltmeter to give a full-scale deflection of 250 V.

(III) A battery with \(\mathscr{E}=12.0 \mathrm{~V}\) and internal resistance \(r=1.0 \Omega\) is connected to two \(7.5 k \Omega\) resistors in series. An ammeter of internal resistance \(0.50 \Omega\) measures the current, and at the same time a voltmeter with internal resistance \(15 k \Omega\) measures the voltage across one of the \(7.5-k \Omega\) resistors in the circuit. What do the ammeter and voltmeter read? What is the % “error” from the current and voltage without meters? Equation transcription: Text transcription: {E}=12.0{~V} r=1.0 Omega 7.5 k Omega 0.50 Omega 15 k Omega 7.5-k Omega

(III) What internal resistance should the voltmeter of Example 19–17 have to be in error by less than 5%?

Problem 65P (III) Two 9.4-K ? resistors are placed in series and connected to a battery. A voltmeter of sensitivity 1000 ?/V is on the 3.0-V scale and reads 1.9 V when placed across either resistor. What is the emf of the battery? (Ignore its internal resistance.)

(III) When the resistor R in Fig. 19–73 is \(35 \Omega\), the high-resistance voltmeter reads 9.7 V. When R is replaced by a \(14.0-\Omega\) resistor, the voltmeter reading drops to 8.1 V. What are the emf and internal resistance of the battery? Equation transcription: Text transcription: 35 Omega 14.0-Omega

Suppose that you wish to apply a 0.25-V potential difference between two points on the human body. The resistance is about \(1800 \Omega\), and you only have a 1.5-V battery. How can you connect up one or more resistors to produce the desired voltage? Equation transcription: Text transcription: 1800 Omega

A three-way lightbulb can produce 50W, 100W, or 150W, at 120 V. Such a bulb contains two filaments that can be connected to the 120 V individually or in parallel (Fig. 19–74). (a) Describe how the connections to the two filaments are made to give each of the three wattages. (b)What must be the resistance of each filament?

Problem 69GP What are the values of effective capacitance which can be obtained by connecting four identical capacitors, each having a capacitance C?

Electricity can be a hazard in hospitals, particularly to patients who are connected to electrodes, such as an ECG. Suppose that the motor of a motorized bed shorts out to the bed frame, and the bed frame’s connection to a ground has broken (or was not there in the first place). If a nurse touches the bed and the patient at the same time, the nurse becomes a conductor and a complete circuit can be made through the patient to ground through the ECG apparatus. This is shown schematically in Fig. 19–75. Calculate the current through the patient. \(10^{4} \Omega\) Equation transcription: Text transcription: 10^{4} Omega

A heart pacemaker is designed to operate at 72 beats/min using a \(6.5-\mu F\) capacitor in a simple RC circuit. What value of resistance should be used if the pacemaker is to fire (capacitor discharge) when the voltage reaches 75% of maximum and then drops to 0 V (72 times a minute)? Equation transcription: Text transcription: 6.5-mu F

Suppose that a person’s body resistance is \(950 \Omega\) (moist skin). () What current passes through the body when the person accidentally is connected to 120 V? (b) If there is an alternative path to ground whose resistance is \(25 \Omega\), what then is the current through the body? (c) If the voltage source can produce at most 1.5 A, how much current passes through the person in case (b)? Equation transcription: Text transcription: 950 Omega 25 Omega

Problem 73GP One way a multiple-speed ventilation fan for a car can be designed is to put resistors in series with the fan motor. The resistors reduce the current through the motor and make it run more slowly. Suppose the current in the motor is 5.0 A when it is connected directly across a 12-V battery. (a) What series resistor should be used to reduce the current to 2.0 A for low-speed operation? (b) What power rating should the resistor have? Assume that the motor’s resistance is roughly the same at all speeds.

A Wheatstone bridge is a type of “bridge circuit” used to make measurements of resistance. The unknown resistance to be measured, \(R_{X}\), is placed in the circuit with accurately known resistances \(R_{1}, R_{2}\), and R? (Fig. 19–76). One of these \(R_{3}\), is a variable resistor which is adjusted so that when the switch is closed momentarily, the ammeter ? shows zero current flow. The bridge is then said to be balanced. (a) Determine \(R_{X}\) in terms of \(R_{1}, R_{2}\), and \(R_{3}\) (b) If a Wheatstone bridge is “balanced” when \(R_{1}-590 \Omega, R_{2}=972 \Omega\), and \(R=78.6 \Omega\), what is the value of the unknown resistance? Equation transcription: Text transcription: R{X} R{1}, R{2} R{3} R{1}-590 Omega, R{2}=972 Omega R=78.6 Omega

The internal resistance of a 1.35-V mercury cell is \(0.030 \Omega\), whereas that of a 1.5-V dry cell is \(0.35 \Omega\). Explain why three mercury cells can more effectively power a 2.5-W hearing aid that requires 4.0 V than can three dry cells. Equation transcription: Text transcription: 0.030 Omega 0.35 Omega

How many \(\frac{1}{2}-W\) resistors, each of the same resistance, must be used to produce an equivalent \(3.2 k \Omega, 3.5-W\) resistor? What is the resistance of each, and how must they be connected? Do not exceed \(P=\frac{1}{2} W\) in each resistor. Equation transcription: Text transcription: frac{1}{2}-W 3.2 k Omega, 3.5-W P=frac{1}{2} W

Problem 77GP A solar cell, 3.0 cm square, has an output of 350 mA at 0.80 V when exposed to full sunlight. A solar panel that delivers close to 1.3 A of current at an emf of 120 V to an external load is needed. How many cells will you need to create the panel? How big a panel will you need, and how should you connect the cells to one another?

The current through the \(4.0-k \Omega\) resistor in Fig. 19–77 is 3.10 mA. What is the terminal voltage \(V_{b a}\) of the “unknown”battery? (There are two answers. Why?) \(4.0-k \Omega\) \(V_{b a}\) \(3.2 k \Omega\) \(1.0 \Omega\) \(8.0 \Omega\) \(12.0 \mathrm{~V}\) Equation transcription: Text transcription: 4.0-k Omega V{b a} 3.2 k Omega 1.0 Omega 8.0 Omega 12.0{~V}

A power supply has a fixed output voltage of 12.0 V, but you need \(V_{T}=3.5 \mathrm{~V}\) output for an experiment. () Using the voltage divider shown in Fig. 19–78, what should \(R_{2}\) be if \(R_{1}\) is \(14.5 \Omega\)? (b) What will the terminal voltage VT be if you connect a load to the 3.5-V output, assuming the load has a resistance of 7.0 ? \(\(R_{1}\)\) \(R_{2}\) \(14.5 \Omega\) \(7.0 \Omega\) \(V_{T}\) \(12.0 \mathrm{~V}\) Equation transcription: Text transcription: V{T}=3.5{~V} R{2} R{1} 14.5 Omega 7.0 Omega V_{T} 12.0{~V}

Problem 80GP A battery produces 40.8 V when 8.40 A is drawn from it, and 47.3 V when 2.80 A is drawn. What are the emf and internal resistance of the battery?

In the circuit shown in Fig. 19–79, the \(33 \Omega\) resistor dissipates 0.80 W. What is battery voltage? \(33 \Omega\) \(68 \Omega\) \(85 \Omega\) Equation transcription: Text transcription: 33 Omega 68 Omega 85 Omega

For the circuit shown in Fig. 19–80, determine () the current through the 16-V battery and (b) the potential difference between points a and b, \(V_{a}-V_{b}\) \(10 k \Omega\) \(13 k \Omega\) \(16 \mathrm{~V}\) \(21 \mathrm{~V}\) \(12 V\) Equation transcription: Text transcription: V{a}-V{b} 10 k Omega 13 k Omega 16{~V} 21{~V} 12 V

The current through the \(20-\Omega\) resistor in Fig. 19–81 does not change whether the two switches S and \(S_{2}\) are both open or both closed. Use this clue to determine the value of the unknown resistance R. \(20-\Omega\) \(S_{2}\ \(S_{1}\) \(10 \Omega\) \(50 \Omega\) \(6.0 \mathrm{~V}\) Equation transcription: Text transcription: 20-Omega S{2} S{1} 10 Omega 50 Omega 6.0{~V}

() What is the equivalent resistance of the circuit shown in Fig. 19–82? [Hint: Redraw the circuit to see series and parallel better.] (b) What is the current in the \(14-\Omega\) resistor? (c) What is the current in the \(12-\Omega\) resistor? (d) What is the power dissipation in the \(4.5-\Omega\)? \(14-\Omega\) \(12-\Omega\) \(4.5-\Omega\) \(6.0 \mathrm{~V}\) Equation transcription: Text transcription: 14-Omega 12-Omega 4.5-Omega 6.0{~V}

(a) A voltmeter and an ammeter can be connected as shown in Fig. a to measure a resistance . If is the voltmeter reading, and is the ammeter reading, the value of will not quite be (as in Ohm's law) because some current goes through the voltmeter. Show that the actual value of is \(\frac{1}{R}=\frac{I}{V}-\frac{1}{R_{r}}\) where is the voltmeter resistance. Note that \(R \approx V / I\) if \(R_{V} \gg R\) (b) A voltmeter and an ammeter can also be connected as shown in Fig. to measure a resistance Show in this case that \(R \approx \frac{V}{I}-R_{A}\) where and are the voltmeter and ammeter readings and \(R_{A}\) is the resistance of the ammeter. Note that \(R \approx V / I\) if \(R_{A} \ll R\). Equation transcription: Text transcription: frac{1}{R}=frac{I}{V}-frac{1}{R{r}} R approx V / I R{V} \gg R R approx frac{V}{I}-R{A} R{A} R{A} ll R

The circuit shown in Fig. 19–84 uses a neon-filled tube as in Fig. 19–23a. This neon lamp has a threshold voltage \(V_{0}\) for conduction, because no current flows until the neon gas in the tube is ionized by a sufficiently strong electric field. Once the threshold voltage is exceeded, the lamp has negligible resistance. The capacitor stores electrical energy, which can be released to flash the lamp. Assume that \(C=0.150 \mu F, R=2.35 \times 10^{6} \Omega, V_{0}=90.0 \mathrm{~V}\), and \(\mathscr{E}=105 \mathrm{~V}\). (a) Assuming the circuit is hooked up to the emf at time t = 0, at what time will the light first flash? (b) If the value of R is increased, will the time you found in part () increase or decrease? (c) The flashing of the lamp is very brief. Why? (d) Explain what happens after the lamp flashes for the first time. \(\mathscr{E}=105 \mathrm{~V}\) Equation transcription:: Text transcription: V{0} C=0.150 mu F, R=2.35 times 10^{6} Omega, V{0}=90.0{~V} {E}=105{~V}

A flashlight bulb rated at \(2.0 \mathrm{~W}\) and \(3.0 V\) is operated by a \(9.0-V\) battery. To light the bulb at its rated voltage and power, a resistor R is connected in series as shown in Fig. 19–85. What value should the resistor have? \(9.0 \mathrm{~V}\) Equation transcription: Text transcription: 2.0{~W} 3.0 V 9.0-V 9.0{~V}

In Fig. 19–86, let \(V=10.0 V\) and \(C_{1}=C_{2}=C_{3}=25.4 \mu \mathrm{F}\). How much energy is stored in the capacitor network () as shown, (b) if the capacitors were all in series, and (c) if the capacitors were all in parallel? \(C_{1}\) \(C_{2}\) \(C_{3}\) Equation transcription: Text transcription: V=10.0 V C{1}=C{2}=C{3}=25.4 mu{F} C{1} C{2} C{3}

A 12.0-V battery, two resistors, and two capacitors are connected as shown in Fig. 19–87. After the circuit has been connected for a long time, what is the charge on each capacitor? \(1.3 k \Omega\) \(2.0 \mathrm{~V}\) \(3.3 k \Omega\) \(12 \mu \Gamma\) \(48 \mu F\) Equation transcription: Text transcription: 1.3 k Omega 2.0{~V} 3.3 k Omega 12 mu Gamma 48 mu F

Determine the current in each resistor of the circuit shown in Fig. 19–88. \(12.00 \mathrm{~V}\) \(6.00 \mathrm{~V}\) \(6.00 \Omega\) \(4.00 \mathrm{~V}\) \(6.80 \Omega\) \(12.00 \Omega\) Equation transcription: Text transcription: 12.00{~V} 6.00{~V} 6.00 Omega 4.00{~V} 6.80 Omega 12.00 Omega

How much energy must a 24-V battery expend to charge a \(0.45-\mu F\) and a capacitor fully when they are placed () in parallel, (b) in series? (c) How much charge flowed from the battery in each case? Equation transcription: Text transcription: 0.45-mu F

Two capacitors, \(C_1 = 2.2\ \mu F\) and \(C_2 = 1.2\ \mu F\), are connected in parallel to a 24-V source as shown in Fig. 19-89a. After they are charged they are disconnected from the source and from each other, and then reconnected directly to each other with plates of opposite sign connected together (see Fig. 19–89b). Find the charge on each capacitor and the potential across each after equilibrium is established (Fig.19–89c).

The switch S in Fig. 19–90 is connected downward so that capacitor \(C_{2}) becomes fully charged by the battery of voltage \(V_{0}\) .If the switch is then connected upward, determine the charge on each capacitor after the switching. \(C_{2}\) \(V_{0}\) \(C_{1}\) Equation transcription: Text transcription: C{2} V{0} C{1}

The performance of the starter circuit in a car can be significantly degraded by a small amount of corrosion on a battery terminal. Figure 19–91a depicts a properly functioning circuit with a battery (\(12.5-V\) emf, \(0.02-\Omega\) internal resistance) attached via corrosion-free cables to a starter motor of resistance \(R_{S}=0.15 \Omega\). Sometime later, corrosion between a battery terminal and a starter cable introduces an extra series resistance of only \(R_{C}=0.10 \Omega\) into the circuit as suggested in Fig. 19–91b. Let P0 be the power delivered to the starter in the circuit free of corrosion, and let P be the power delivered to the circuit with corrosion. Determine the ratio \(P / P_{0}\). Equation transcription: Text transcription: 12.5-V 0.02-Omega R{S}=0.15 Omega R{C}=0.10 Omega P / P{0}

Problem 95GP The variable capacitance of an old radio tuner consists of four plates connected together placed alternately between four other plates, also connected together (Fig. 19–92). Each plate is separated from its neighbor by 1.6 mm of air. One set of plates can move so that the area of overlap of each plate varies from 2.0 cm2 to 9.0 cm2. (a) Are these seven capacitors connected in series or in parallel? (b) Determine the range of capacitance values.

Problem 96GP A 175-pF capacitor is connected in series with an unknown capacitor, and as a series combination they are connected to a 25.0-V battery. If the 175-pF capacitor stores 125 pC of charge on its plates, what is the unknown capacitance?

In the circuit shown in Fig. 19–93, \(C_{1}=1.0 \mu F, C_{1}=2.0 \mu F\), and a voltage \(V_{a b}=24\) V is applied across points a and b. After \(C_{1}\) is fully charged, the switch is thrown to the right. What is the final charge and potential difference on each capacitor? \(C_{1}\) \(C_{2}\) \(C_{3}\) Equation transcription: Text transcription: C{1}=1.0 mu F, C{1}=2.0 mu F V{a b}=24 C{1} C{2} C{3}

Calculate the terminal voltage for a battery with an internal resistance of and an emf of 6.00 V when the battery is connected in series with (a) a resistor, and (b) a resistor

Four 1.50-V cells are connected in series to a lightbulb. If the resulting current is 0.45 A, what is the internal resistance of each cell, assuming they are identical and neglecting the resistance of the wires?

What is the internal resistance of a 12.0-V car battery whose terminal voltage drops to 8.8 V when the starter motor draws 95 A? What is the resistance of the starter?

A and an resistor are connected in series with a 12-V battery. What is the voltage across the resistor

Three lightbulbs and three lightbulbs are connected in series. (a) What is the total resistance of the circuit? (b) What is the total resistance if all six are wired in parallel?

(II) Suppose that you have a \(580-\Omega\), a \(790-\Omega\), and a \(1.20-k\Omega\) resistor. What is (a) the maximum, and (b) the minimum resistance you can obtain by combining these?

How many resistors must be connected in series to give an equivalent resistance to five resistors connected in parallel?

Design a voltage divider (see Example 193) that would provide one-fifth (0.20) of the battery voltage across Fig. 196. What is the ratio

Suppose that you have a 9.0-V battery and wish to apply a voltage of only 3.5 V. Given an unlimited supply of resistors, how could you connect them to make a voltage divider that produces a 3.5-V output for a 9.0-V input?

Three resistors can be connected together in four different ways, making combinations of series and/or parallel circuits. What are these four ways, and what is the net resistance in each case?

(II) A battery with an emf of 12.0 V shows a terminal voltage of 11.8 V when operating in a circuit with two lightbulbs, each rated at 4.0 W (at 12.0 V), which are connected in parallel. What is the battery’s internal resistance?

Eight identical bulbs are connected in series across a 120-V line. (a) What is the voltage across each bulb? (b) If the current is 0.45 A, what is the resistance of each bulb, and what is the power dissipated in each?

Eight bulbs are connected in parallel to a 120-V source by two long leads of total resistance If 210 mA flows through each bulb, what is the resistance of each, and what fraction of the total power is wasted in the leads?

A close inspection of an electric circuit reveals that a resistor was inadvertently soldered in the place where a resistor is needed. How can this be fixed without removing anything from the existing circuit?

Eight 7.0-W Christmas tree lights are connected in series to each other and to a 120-V source. What is the resistance of each bulb?

Determine (a) the equivalent resistance of the circuit shown in Fig. 1948, (b) the voltage across each resistor, and (c) the current through each resistor.

A 75-W, 120-V bulb is connected in parallel with a 25-W, 120-V bulb. What is the net resistance?

(a) Determine the equivalent resistance of the ladder of equal resistors shown in Fig. 1949. In other words, what resistance would an ohmmeter read if connected between points A and B? (b) What is the current through each of the three resistors on the left if a 50.0-V battery is connected between points A and B?

What is the net resistance of the circuit connected to the battery in Fig. 1950?

Calculate the current through each resistor in Fig. 1950 if each resistance and What is the potential difference between points A and B?

Two resistors when connected in series to a 120-V line use one-fourth the power that is used when they are connected in parallel. If one resistor is what is the resistance of the other?

Three equal resistors (R) are connected to a battery as shown in Fig. 1951. Qualitatively, what happens to (a) the voltage drop across each of these resistors, (b) the current flow through each, and (c) the terminal voltage of the battery, when the switch S is opened, after having been closed for a long time? (d) If the emf of the battery is 9.0 V, what is its terminal voltage when the switch is closed if the internal resistance r is and (e) What is the terminal voltage when the switch is open?

A and a resistor are connected in parallel; this combination is connected in series with a resistor. If each resistor is rated at 0.5 W (maximum without overheating), what is the maximum voltage that can be applied across the whole network?

Consider the network of resistors shown in Fig. 1952. Answer qualitatively: (a) What happens to the voltage across each resistor when the switch S is closed? (b) What happens to the current through each when the switch is closed? (c) What happens to the power output of the battery when the switch is closed? (d) Let and Determine the current through each resistor before and after closing the switch. Are your qualitative predictions confirmed?

(I) Calculate the current in the circuit of Fig. 19–53, and show that the sum of all the voltage changes around the circuit is zero.

Determine the terminal voltage of each battery in Fig. 1954.

For the circuit shown in Fig. 1955, find the potential difference between points a and b. Each resistor has and each battery is 1.5 V.

(II) Determine the magnitudes and directions of the currents in each resistor shown in Fig. 19–56. The batteries have emfs of \(\mathscr{E}_1 = 9.0\ V\) and \(\mathscr{E}_2 = 12.0\ V\) and the resistors have values of \(R_1 = 25\ \Omega\), \(R_2 = 68\ \Omega\), and \(R_3 = 35\ \Omega\). (a) Ignore internal resistance of the batteries. (b) Assume each battery has internal resistance \(r = 1.0\ \Omega\).

(a) What is the potential difference between points a and d in Fig. 1957 (similar to Fig. 1913, Example 198), and (b) what is the terminal voltage of each battery?

Calculate the magnitude and direction of the currents in each resistor of Fig. 1958.

Determine the magnitudes and directions of the currents through and in Fig. 19 R 59.

Repeat Problem 31, now assuming that each battery has an internal resistance

A network of five equal resistors R is connected to a battery as shown in Fig. 1960. Determine the current I that flows out of the battery. (b) Use the value determined for I to find the single resistor that is equivalent to the five-resistor network.

(III) (a) Determine the currents \(I_1\), \(I_2\), and \(I_3\) in Fig. 19-61. Assume the internal resistance of each battery is \(r = 1.0\ \Omega\). (b) What is the terminal voltage of the 6.0-V battery?

What would the current be in Fig. 1961 if the resistor is shorted out (resistance )? Let = 0 r = 1.0 . I1 12-

Suppose two batteries, with unequal emfs of 2.00 V and 3.00 V, are connected as shown in Fig. 1962. If each internal resistance is and what is the voltage across the resistor R?

A battery for a proposed electric car is to have three hundred 3-V lithium ion cells connected such that the total voltage across all of the cells is 300 V. Describe a possible connection configuration (using series and parallel connections) that would meet these battery specifications.

(a) Six capacitors are connected in parallel. What is the equivalent capacitance? (b) What is their equivalent capacitance if connected in series?

A and a capacitor are connected in series, and this combination is connected in parallel with a capacitor (see Fig. 1963). What is the net capacitance?

If 21.0 V is applied across the whole network of Fig. 1963, calculate (a) the voltage across each capacitor and (b) the charge on each capacitor.

The capacitance of a portion of a circuit is to be reduced from 2900 pF to 1200 pF. What capacitance can be added to the circuit to produce this effect without removing existing circuit elements? Must any existing connections be broken to accomplish this?

An electric circuit was accidentally constructed using a capacitor instead of the required value. Without removing the capacitor, what can a technician add to correct this circuit?

Consider three capacitors, of capacitance 3200 pF, 5800 pF, and What maximum and minimum capacitance can you form from these? How do you make the connection in each case?

Determine the equivalent capacitance between points a and b for the combination of capacitors shown in Fig. 1964.

What is the ratio of the voltage across capacitor in Fig. 1965 to the voltage across capacitor V2 C2?

A and a capacitor are connected in series to a 9.0-V battery. Calculate (a) the potential difference across each capacitor and (b) the charge on each. (c) Repeat parts (a) and (b) assuming the two capacitors are in parallel.

A circuit contains a single 250-pF capacitor hooked across a battery. It is desired to store four times as much energy in a combination of two capacitors by adding a single capacitor to this one. How would you hook it up, and what would its value be?

(II) Suppose three parallel-plate capacitors, whose plates have areas \(A_1, A_2\), and \(A_3\) and separations \(d_1, d_2\), and \(d_3\) are connected in parallel. Show, using only Eq. 17–8, that Eq. 19–5 is valid.

Two capacitors connected in parallel produce an equivalent capacitance of but when connected in series the equivalent capacitance is only What is the individual capacitance of each capacitor?

Given three capacitors, and what arrangement of parallel and series connections with a 12-V battery will give the minimum voltage drop across the capacitor? What is the minimum voltage drop?

In Fig. 1966, suppose (a) Determine the equivalent capacitance between points a and b. (b) Determine the charge on each capacitor and the potential difference across each in terms of V.

Estimate the value of resistances needed to make a variable timer for intermittent windshield wipers: one wipe every 15 s, 8 s, 4 s, 2 s, 1 s. Assume the capacitor used is on the order of See Fig. 19 1 mF. 67.

(II) Electrocardiographs are often connected as shown in Fig. 19–68. The lead wires to the legs are said to be capacitively coupled. A time constant of 3.0 s is typical and allows rapid changes in potential to be recorded accurately. If \(C = 3.0\ \mu F\), what value must R have? [Hint: Consider each leg as a separate circuit.]

In Fig. 1969 (same as Fig. 1920a), the total resistance is and the batterys emf is 24.0 V. If the time constant is measured to be calculate (a) the total capacitance of the circuit and (b) the time it takes for the voltage across the resistor to reach 16.0 V after the switch is closed.

Two capacitors, two resistors, and a 16.0-V source are connected in series. Starting from the uncharged state, how long does it take for the current to drop from its initial value to 1.50 mA?

The RC circuit of Fig. 1970 (same as Fig. 1921a) has and The capacitor is at voltage at when the switch is closed. How long does it take the capacitor to discharge to 0.25% of its initial voltage?

Consider the circuit shown in Fig. 1971, where all resistors have the same resistance R. At with the capacitor C uncharged, the switch is closed. (a) At the three currents can be determined by analyzing a simpler, but equivalent, circuit. Draw this simpler circuit and use it to find the values of and at (b) At the currents can be determined by analyzing a simpler, equivalent circuit. Draw this simpler circuit and implement it in finding the values of and at (c) At what is the potential difference across the capacitor?

Two resistors and two uncharged capacitors are arranged as shown in Fig. 1972. Then a potential difference of 24 V is applied across the combination as shown. (a) What is the potential at point a with switch S open? (Let at the negative terminal of the source.) (b) What is the potential at point b with the switch open? (c) When the switch is closed, what is the final potential of point b? (d) How much charge flows through the switch S after it is closed?

(a) An ammeter has a sensitivity of What current in the galvanometer produces full-scale deflection? (b) What is the resistance of a voltmeter on the 250-V scale if the meter sensitivity is

An ammeter whose internal resistance is reads 5.25 mA when connected in a circuit containing a battery and two resistors in series whose values are and What is the actual current when the ammeter is absent?

A milliammeter reads 35 mA full scale. It consists of a resistor in parallel with a galvanometer. How can you change this ammeter to a voltmeter giving a full-scale reading of 25 V without taking the ammeter apart? What will be the sensitivity of your voltmeter?

A galvanometer has an internal resistance of and deflects full scale for a current. Describe how to use this galvanometer to make (a) an ammeter to read currents up to 25 A, and (b) a voltmeter to give a full-scale deflection of 250 V

A battery with and internal resistance is connected to two resistors in series. An ammeter of internal resistance measures the current, and at the same time a voltmeter with internal resistance measures the voltage across one of the resistors in the circuit. What do the ammeter and voltmeter read? What is the % error from the current and voltage without meters?

What internal resistance should the voltmeter of Example 1917 have to be in error by less than 5%?

Two resistors are placed in series and connected to a battery.A voltmeter of sensitivity is on the 3.0-V scale and reads 1.9 V when placed across either resistor. What is the emf of the battery? (Ignore its internal resistance.)

When the resistor R in Fig. 1973 is the highresistance voltmeter reads 9.7 V. When R is replaced by a resistor, the voltmeter reading drops to 8.1 V. What are the emf and internal resistance of the battery?

Suppose that you wish to apply a 0.25-V potential difference between two points on the human body. The resistance is about and you only have a 1.5-V battery. How can you connect up one or more resistors to produce the desired voltage

A three-way lightbulb can produce 50 W, 100 W, or 150 W, at 120 V. Such a bulb contains two filaments that can be connected to the 120 V individually or in parallel (Fig.1974). (a) Describe how the connections to the two filaments are made to give each of the three wattages. (b) What must be the resistance of each filament?

What are the values of effective capacitance which can be obtained by connecting four identical capacitors, each having a capacitance C?

Electricity can be a hazard in hospitals, particularly to patients who are connected to electrodes, such as an ECG. Suppose that the motor of a motorized bed shorts out to the bed frame, and the bed frames connection to a ground has broken (or was not there in the first place). If a nurse touches the bed and the patient at the same time, the nurse becomes a conductor and a complete circuit can be made through the patient to ground through the ECG apparatus. This is shown schematically in Fig. 1975. Calculate the current through the patient.

A heart pacemaker is designed to operate at using a capacitor in a simple RC circuit. What value of resistance should be used if the pacemaker is to fire (capacitor discharge) when the voltage reaches 75% of maximum and then drops to 0 V (72 times a minute)?

Suppose that a person’s body resistance is \(95 \ \Omega\) (moist skin). (a) What current passes through the body when the person accidentally is connected to 120 V? (b) If there is an alternative path to ground whose resistance is \(25 \ \Omega\) , what then is the current through the body? (c) If the voltage source can produce at most 1.5 A, how much current passes through the person in case (b)?

One way a multiple-speed ventilation fan for a car can be designed is to put resistors in series with the fan motor. The resistors reduce the current through the motor and make it run more slowly. Suppose the current in the motor is 5.0 A when it is connected directly across a 12-V battery. (a) What series resistor should be used to reduce the current to 2.0 A for low-speed operation? (b) What power rating should the resistor have? Assume that the motors resistance is roughly the same at all speeds.

A Wheatstone bridge is a type of bridge circuit used to make measurements of resistance. The unknown resistance to be measured, is placed in the circuit with accurately known resistances and (Fig. 1976). One of these, is a variable resistor which is adjusted so that when the switch is closed momentarily, the ammeter shows zero current flow. The bridge is then said to be balanced. (a) Determine in terms of and (b) If a Wheatstone bridge is balanced when and what is the value of the unknown resistance?

The internal resistance of a 1.35-V mercury cell is whereas that of a 1.5-V dry cell is Explain why three mercury cells can more effectively power a 2.5-W hearing aid that requires 4.0 V than can three dry cells

How many resistors, each of the same resistance, must be used to produce an equivalent 3.5-W resistor? What is the resistance of each, and how must they be connected? Do not exceed in each resistor.

A solar cell, 3.0 cm square, has an output of 350 mA at 0.80 V when exposed to full sunlight. A solar panel that delivers close to 1.3 A of current at an emf of 120 V to an external load is needed. How many cells will you need to create the panel? How big a panel will you need, and how should you connect the cells to one another?

The current through the resistor in Fig. 1977 is 3.10 mA. What is the terminal voltage of the unknownbattery? (There are two answers. Why?)

A power supply has a fixed output voltage of 12.0 V, but you need output for an experiment. (a) Using the voltage divider shown in Fig. 1978, what should be if is (b) What will the terminal voltage be if you connect a load to the 3.5-V output, assuming the load has a resistance of 7.0 ?

A battery produces 40.8 V when 8.40 A is drawn from it, and 47.3 V when 2.80 A is drawn. What are the emf and internal resistance of the battery?

In the circuit shown in Fig. 1979, the resistor dissipates 0.80 W. What is the battery voltage?

For the circuit shown in Fig. 1980, determine (a) the current through the 16-V battery and (b) the potential difference between points a and b, Va - Vb .

The current through the resistor in Fig. 1981 does not change whether the two switches and are both open or both closed. Use this clue to determine the value of the unknown resistance R

(a) What is the equivalent resistance of the circuit shown in Fig. 1982? [Hint: Redraw the circuit to see series and parallel better.] (b) What is the current in the resistor? (c) What is the current in the resistor? (d) What is the power dissipation in the resistor?

(a) A voltmeter and an ammeter can be connected as shown in Fig. 1983a to measure a resistance R. If V is the voltmeter reading, and I is the ammeter reading, the value of R will not quite be (as in Ohms law) because some current goes through the voltmeter. Show that the actual value of R is where is the voltmeter resistance. Note that if (b) A voltmeter and an ammeter can also be connected as shown in Fig. 1983b to measure a resistance R. Show in this case that where V and I are the voltmeter and ammeter readings and is the resistance of the ammeter. Note that if RA V R.

The circuit shown in Fig. 19–84 uses a neon-filled tube as in Fig. 19–23a. This neon lamp has a threshold voltage \(V_0\) for conduction, because no current flows until the neon gas in the tube is ionized by a sufficiently strong electric field. Once the threshold voltage is exceeded, the lamp has negligible resistance. The capacitor stores electrical energy, which can be released to flash the lamp. Assume that \(C = 0.150\ \mu F\), \(R = 2.35 \times 10^6\ \Omega,\ V_0 = 90.0\ V,\ \text{and}\ \mathscr{E} = 105\ V\). (a) Assuming the circuit is hooked up to the emf at time t = 0, at what time will the light first flash? (b) If the value of R is increased, will the time you found in part (a) increase or decrease? (c) The flashing of the lamp is very brief.Why? (d) Explain what happens after the lamp flashes for the first time.

A flashlight bulb rated at 2.0 W and 3.0 V is operated by a 9.0-V battery. To light the bulb at its rated voltage and power, a resistor R is connected in series as shown in Fig. 1985. What value should the resistor have?

In Fig. 1986, let and How much energy is stored in the capacitor network (a) as shown, (b) if the capacitors were all in series, and (c) if the capacitors were all in parallel?

A 12.0-V battery, two resistors, and two capacitors are connected as shown in Fig. 1987. After the circuit has been connected for a long time, what is the charge on each capacitor?

Determine the current in each resistor of the circuit shown in Fig. 1988.

How much energy must a 24-V battery expend to charge a and a capacitor fully when they are placed (a) in parallel, (b) in series? (c) How much charge flowed from the battery in each case?

Two capacitors, and are connected in parallel to a 24-V source as shown in Fig. 1989a. After they are charged they are disconnected from the source and from each other, and then reconnected directly to each other with plates of opposite sign connected together (see Fig. 1989b). Find the charge on each capacitor and the potential across each after equilibrium is established (Fig.1989c)

The switch S in Fig. 1990 is connected downward so that capacitor becomes fully charged by the battery of voltage If the switch is then connected upward, determine the charge on each capacitor after the switching

The performance of the starter circuit in a car can be significantly degraded by a small amount of corrosion on a battery terminal. Figure 1991a depicts a properly functioning circuit with a battery (12.5-V emf, internal resistance) attached via corrosion-free cables to a starter motor of resistance Sometime later, corrosion between a battery terminal and a starter cable introduces an extra series resistance of only into the circuit as suggested in Fig. 1991b. Let be the power delivered to the starter in the circuit free of corrosion, and let P be the power delivered to the circuit with corrosion. Determine the ratio PP0 .

The variable capacitance of an old radio tuner consists of four plates connected together placed alternately between four other plates, also connected together (Fig. 1992). Each plate is separated from its neighbor by 1.6 mm of air. One set of plates can move so that the area of overlap of each plate varies from to (a) Are these seven capacitors connected in series or in parallel? (b) Determine the range of capacitance values.

A 175-pF capacitor is connected in series with an unknown capacitor, and as a series combination they are connected to a 25.0-V battery. If the 175-pF capacitor stores 125 pC of charge on its plates, what is the unknown capacitance?

In the circuit shown in Fig. 1993, and a voltage is applied across points a and b. After is fully charged, the switch is thrown to the right. What is the final charge and potential difference on each capacitor?