A Wheatstone bridge is a type of “bridge circuit” used to

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.

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.

If all you have is a \(120-\mathrm{V}\) line, would it be possible to light several 6-V lamps without burning them out? How?

Problem 4Q Two lightbulbs of resistance R1 and R2 (R2 > R1) and a battery are all connected in series. Which bulb is brighter? What if they are connected in parallel? Explain.

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

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.

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 applying Kirchhoffs loop rule (such as in Fig. 19-35), does the sign (or direction) of a battery's emf depend on the direction of current through the battery? What about the terminal voltage?

Given the circuit shown in Fig. , use the words "increases," "decreases," or "stays the same" to complete the following statements: (a) If \(R_{7}\) increases, the potential difference between A and E_____. Assume no resistance in and \(\varepsilon\) (b) If \(R_{7}\) increases, the potential difference between A and E ______. Assume and \(\varepsilon\) have resistance. (c) If \(R_{7}\) increases, the voltage drop across \(R_{4}\)_______________. If \(R_{2}\) decreases, the current through \(R_{1}\)__________________. (e) If \(R_{2}\) decreases, the current through \(R_{6}\)___________________. If \(R_{2}\) decreases, the current through \(R_{3}\)___________________. (g) If \(R_{5}\) increases, the voltage drop across \(R_{2}\)________________. If \(R_{5}\) increases, the voltage drop across \(R_{4}\)_______________. (i) If \(R_{2}, R_{5} \text { and } R_{7}\) increase, \(\varepsilon_{(r=0)}\)______________________. Equation Transcription: ? ? Text Transcription: R7 ? \varepsilon R7 ? \varepsilon R7 R4 R2 R1 R2 R6 R2 R3 R5 R2 R5 R4 R2,R5 and R7 \varepsilon_(r=0)

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?

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

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

Problem 15Q Suppose three identical capacitors are connected to a battery. Will they store more energy if connected in series or in parallel?

Design a circuit in which two different switches of the type shown in Fig. 19-38 can be used to operate the same lightbulb from opposite sides of a room.

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?

Problem 19Q 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?

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

Problem 21Q What would happen if you mistakenly used an ammeter where you needed to use a voltmeter?

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

Problem 23Q A voltmeter connected across a resistor always reads less than the actual voltage (i.e., when the meter is not present). Explain.

Problem 24Q 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?

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?

Electrocardiographs are often connected as shown in Fig. 19-55. The leads 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 ]

A three-way lightbulb can produce \(50 \mathrm{~W}, 100 \mathrm{~W}\), or \(150 \mathrm{~W}\), at \(120 \mathrm{~V}\). Such a bulb contains two filaments that can be connected to the \(120 \mathrm{~V}\) individually or in parallel. (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 1P Calculate the terminal voltage for a battery with an internal resistance of 0.900? and an emf of 8.50 V when the battery is connected in series with (a) an 81.0-? resistor, and (b) an 810-? resistor.

(II) What is the internal resistance of a \(12.0-\mathrm{V}\) car battery whose terminal voltage drops to \(8.4 \mathrm{~V}\) when the starter draws \(75 \mathrm{~A}\)? What is the resistance of the starter?

Problem 73GP What are the values of effective capacitance which can be obtained by connecting four identical capacitors, each having a capacitance C?

Problem 4P A 1.5-V dry cell can be tested by connecting it to a low-resistance ammeter. It should be able to supply at least 22 A. What is the internal resistance of the cell in this case, assuming it is much greater than that of the ammeter?

Problem 75GP 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?

(I) Four \(240-\Omega\) lightbulbs are connected in series. What is the total resistance of the circuit? What is their resistance if they are connected in parallel?

Problem 6P Three 45-? lightbulbs and three 75-? lightbulbs are connected in series. (a) What is the total resistance of the circuit? (b) What is their resistance if all six are wired in parallel?

Problem 6Q With two identical lightbulbs and two identical batteries, how would you arrange the bulbs and batteries in a circuit to get the maximum possible total power out? (Assume the batteries have negligible internal resistance.)

Problem 7P A 650-? and a 2200-? resistor are connected in series with a 12-V battery. What is the voltage across the 2200-? resistor?

Problem 8P Given only one 25-? and one 35-? resistor, list all possible values of resistance that can be obtained.

The circuit shown in Fig. 19-67 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 \(\mathrm{C}=0.150 \mu \mathrm{F}, \mathrm{R}=2.35 \times 10^{\circ} \Omega, \mathrm{V}_{0}=90.0 \mathrm{~V}\) 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 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?

The current through the 20- \(\Omega\) resistor in Fig. 19-68 does not change whether the two switches \(\mathrm{S}_1\) and \(\mathrm{S}_2\) are both open or both closed. Use this clue to determine the value of the unknown resistance R.

Problem 9P Suppose that you have a 680-?, a 940-?, and a 1.20-k? resistor. What is (a) the maximum, and (b) the minimum resistance you can obtain by combining these?

(II) Suppose that you have a 6.0-V battery and you wish to apply a voltage of only 4.0 V. Given an unlimited supply of \(1.0-\Omega\) resistors, how could you connect them so as to make a “voltage divider” that produces a 4.0-V output for a 6.0-V input?

(a) A voltmeter and an ammeter can be connected as shown in Fig. 19-71a to measure a resistance R. If V is the voltmeter reading, and I is the ammeter reading, the value of R will be V / I (as in Ohm’s law) because some current goes through the voltmeter. Show that the actual value of R is given by \(\frac{1}{R}=\frac{1}{V}-\frac{1}{R_{0}}\) Where \(R_{V}\) is the voltmeter resistance. Note that \(R \approx V / I \text { if } R \gg R\). (b) A voltmeter and an ammeter can also be connected as shown in Fig. 19-71b to measure a resistance R. Shown in this case that \(R=\frac{I}{V}-R_{A}\) where V and I are the voltmeter and ammeter readings and \(R_{A}\) is the resistance of the ammeter. Note that \(R \approx V / I \text { if } R_{A} \ll R\).

Problem 11P Three 240-? 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?

Problem 12P A battery with an emf of 12.0 V shows a terminal voltage of 11.8V when operating in a circuit with two lightbulbs rated at 3.0 W (at 12.0 V) which are connected in parallel. What is the battery’s internal resistance?

Problem 13P Eight identical lights are connected in series across a 110-V line. (a) What is the voltage across each bulb? (b) If the current is 0.50 A, what is the resistance of each bulb, and what is the power dissipated in each?

Problem 14P Eight lights are connected in parallel to a 110-V source by two long leads of total resistance 1.6 ?. If 240 mA flows through each bulb, what is the resistance of each, and what fraction of the total power is wasted in the leads?

Compare and discuss the formulas for resistors and for capacitors when connected in series and in parallel.

Problem 15P Eight 7.0-W Christmas tree lights are connected in series to each other and to a 110-V source. What is the resistance of each bulb?

(II) A close inspection of an electric circuit reveals that a \(480-\Omega\) resistor was inadvertently soldered in the place where a \(320-\Omega\) resistor is needed. How can this be fixed without removing anything from the existing circuit?

Figure 19–37 is a diagram of a capacitor (or condenser) microphone. The changing air pressure in a sound wave causes one plate of the capacitor C to move back and forth. Explain how a current of the same frequency as the sound wave is produced.

Determine (a) the equivalent resistance of the circuit shown in Fig. 19–39, and (b) the voltage across each resistor.

Problem 18P A 75-W, 110-V bulb is connected in parallel with a 40-W, 110-V bulb. What is the net resistance?

(III) Consider the network of resistors shown in Fig. 19–40. 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 \(R_{1}=R_{2}=R_{3}=R_{4}=125 \Omega \text { and } V=22.0 \mathrm{~V}\). Determine the current through each resistor before and after closing the switch. Are your qualitative predictions confirmed? Equation Transcription: Text Transcription: R1=R2=R3=R4=125 \Omega and V=22.0 V

(III) What is the net resistance of the circuit connected to the battery in Fig. 19-41? Each resistance has \(R=2.8 \mathrm{k} \Omega\)

(III) Three equal resistors (R) are connected to a battery as shown in Fig. 19–42. 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 15.0 V, what is its terminal voltage when the switch is closed if the internal resistance is \(0.50 \Omega \text { and } R=5.50 \Omega\)? (e) What is the terminal voltage when the switch is open? Equation Transcription: Text Transcription: 0.50 \Omega and R=5.50 \Omega

(III) A \(2.8-\mathrm{k} \Omega\) and a \(2.1-\mathrm{k} \Omega\) resistor are connected in parallel; this combination is connected in series with a \(1.8-\mathrm{k} \Omega\) resistor. If each resistor is rated at \(\frac{1}{2} \mathrm{~W}\) (maximum without overheating), what is the maximum voltage that can be applied across the whole network?

(I) Calculate the current in the circuit of Fig. 19–43 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. 19–44.

(II) (a) What is the potential difference between points a and d in Fig. 19–45 (same circuit as Fig. 19-13, Example 19-8), and (b) what is the terminal voltage of each battery?

(II) For the circuit shown in Fig. 19–46, find the potential difference between points a and b. Each resistor has \( Equation Transcription: Text Transcription: R=75 \Omega

(II) Determine the magnitudes and directions of the currents through \(R_{1} \text { and } R_{2}\) in Fig. 19–47. Equation Transcription: Text Transcription: R1 and R2

(II) Repeat Problem 27, now assuming that each battery has an internal resistance \(r=1.2 \Omega\). Equation Transcription: Text Transcription: r=1.2 \Omega

(II) Determine the magnitudes and directions of the currents in each resistor shown in Fig. 19–48. The batteries have emfs of \(\varepsilon_{1}=9.0 \mathrm{~V} \text { and } \varepsilon_{2}=12-0 \mathrm{~V}\) and the resistors have values of \(R_{1}=25 \Omega, R_{2}=18 \Omega, \text { and } R_{3}=35 \Omega\) Equation Transcription: Text Transcription: \varepsilon_=9.0 V and \varepsilon_=12-0 V R1=25 \Omega , R2=18 \Omega, and R3=35 \Omega

(II) Repeat Problem 29, assuming each battery has internal resistance \(r=1.0 \Omega\) Equation Transcription: Text Transcription: r=1.0 \Omega

(II) Calculate the currents in each resistor of Fig. 19–49. Equation Transcription: Text Transcription: 12 \Omega 2 \Omega 6 \Omega 8 \Omega 10 \Omega

(III) (a) Determine the currents \(I_{1}, I_{2}, \text { and } I_{3}\) in Fig. 19–50. 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, and I_3 r=1.0 \Omega 6.0-V

(III) What would the current \(I_{1}\) be in Fig. 19–50 if the \(12-\Omega\) resistor is shorted out? 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 \(2.00 \mathrm{~V} \text { and } 3.00 \mathrm{~V}\), are connected as shown in Fig. . If each internal resistance is \(r=0.100 \Omega, \text { and } R=4.00 \Omega\), what is the voltage across the resistor FIGURE 9-51 Problem 34. Equation Transcription: Text Transcription: 2.00 V and 3.00 V r=0.100 \Omega, and R=4.00 \Omega

Problem 35P (a) Six 4.7-?F capacitors are connected in parallel. What is the equivalent capacitance? (b) What is then-equivalent capacitance if connected in series?

Problem 36P You have three capacitors, of capacitance 3200 pF, 7500 pF, and 0.0100 ?F. What maximum and minimum capacitance can you form from these? How do you make the connection in each case?

(I) A \(3.00-\mu \mathrm{F}\) and a \(4.00-\mu \mathrm{F}\) capacitor are connected in series, and this combination is connected in parallel with a \(2.00-\mu \mathrm{F}\) capacitor (see Fig. 19-52). What is the net capacitance?

(II) If \(26.0 \mathrm{~V}\) is applied across the whole network of Fig. , calculate the voltage across each capacitor. FIGURE 19-52 Problem 37 and 38. Equation Transcription: Text Transcription: 26.0 V

Problem 39P The capacitance of a portion of a circuit is to be reduced from 4800 pF to 2900 pF. What capacitance can be added to the circuit to produce this effect without removing existing circuit elements? Must any existing connections be broken in the process?

(II) An electric circuit was accidentally constructed using a \(5.0-\mu \mathrm {F}\) capacitor instead of the required \(16-\mu \mathrm {F}\) value. Without removing the \(5.0-\mu \mathrm {F}\) capacitor, what can a technician add to correct this circuit?

Determine the equivalent capacitance of the circuit shown in Fig. 19-53.

(II) In Fig. 19-53, if \(C_1=C_2=2 C_3=22.6 \mu \mathrm{F}\), how much charge is stored on each capacitor when V=45.0 V ?

(II) In Fig. , suppose \(C_{1}=C_{2}=C_{3}=16.0 \mu F\). If the charge on \(C_{2}\) is \(Q_{2}=24.0 \mu C\), determine the charge on each of the other capacitors, the voltage across each capacitor, and the voltage V across the entire combination.

(II) In Fig. , let \(V=78 \mathrm{~V} \text { and } C_{1}=C_{2}=C_{3}=7.2 \mu \mathrm{F}\), How much energy is stored in the capacitor network? FIGURE 19-52 Problem 41. 42, 43, and 44 Equation Transcription: Text Transcription: V=78 V and C_{1}=C_{2}=C_{3}=7.2 \mu F

Problem 45P A 0 .40-?F and a 0.60-?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.

(II) Three conducting plates, each of area , are connected as shown in Fig. . (a) Are the two capacitors formed connected in series or in parallel? (b) Determine as a function of \(d_{1}, d_{2}, \text { and } A\). Assume \(d_{1}+d_{2}\) is much less than the dimensions of the plates. FIGURE 19-54 Problem 46. Equation Transcription: Text Transcription: d_{1}, d_{2}, and A d_{1}+d_{2}

Problem 48P A 185-pF capacitor is connected in series with an unknown capacitance, and as a series combination they are connected to a battery with an emf of 25.0 V. If the 185-pF capacitor stores 125 pC of charge on its plates, what is the unknown capacitance?

(II) In Fig. (same as Fig. ), 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 \(35.0 \mu s\), calculate the total capacitance of the circuit and the time it takes for the voltage across the resistor to reach \(16.0 V\) after the switch is closed. FIGURE 19-56 Problem 50. Equation Transcription: Text Transcription: 15.0 k \Omega 24.0 V 35.0 \mu s 16.0 V

(II) The circuit of Fig. (same as Fig. a) has \(R=6.7 k \Omega \text { and } C=3.0 \mu F\). The capacitor is at voltage \(V_{0} \text { at } t=0\), when the switch is closed. How long does it take the discharge to voltage? FIGURE 19-57 Problem 51. Equation Transcription: Text Transcription: R=6.7 k \Omega and C=3.0 \mu F V_{0} at t=0

(III) Two resistors and two uncharged capacitors are arranged as shown in Fig. Then a potential difference of is applied across the combination as shown. (a) What is the potential at point a with switch open? (Let \(V=0\) at the negative terminal of the source.) (b) What is the potential at point with the switch open? (c) When the switch is closed, what is the final potential of point b? (d) How much average flows through switch S after it is closed? FIGURE 19-58 Problem 52. Equation Transcription: Text Transcription: V=0

(I) What is the resistance of a voltmeter on the 250-V scale if the meter sensitivity is \(30,000 \Omega/\mathrm {V}\)?

Problem 54P An ammeter has a sensitivity of 20,000 ?/V. What current in the galvanometer produces full-scale deflection?

(II) A galvanometer has an internal resistance of \(30 \ \Omega\) and deflects full scale for a \(50-\muA\) current. Describe how to use this galvanometer to make (a) an ammeter to read currents up to 30 A, and (b) a voltmeter to give a full-scale deflection of 250 V.

Problem 56P A galvanometer has a sensitivity of 35k ?/V and internal resistance 20.0 ?. How could you make this into (a) an ammeter that reads 2.0 A full scale, or (b) a voltmeter reading 1.00 V full scale?

Problem 57P A milliammeter reads 10 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 10 V without taking the ammeter apart? What will be the sensitivity (?/V) of your voltmeter?

(II) An ammeter whose internal resistance is \(63 \Omega\) reads \(5.25 \mathrm{~mA}\) when connected in a circuit containing a battery and two resistors in series whose values are \(750 \Omega\) and \(480 \Omega\). What is the actual current when the ammeter is absent?

Problem 58P A 45-V battery of negligible internal resistance is connected to a 38-k? and a 27-k? resistor in series. What reading will a voltmeter, of internal resistance 95 k?, give when used to measure the voltage across each resistor? What is the percent inaccuracy due to meter resistance for each case?

Problem 61P 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 2.0 V when placed across either resistor. What is the emf of the battery? (Ignore its internal resistance.)

(II) A battery with \(\mathscr{\mathscr { E }}=12.0 \mathrm{~V}\) and internal resistance \(r=1.0 \Omega\) is connected to two \(9.0-\mathrm{k} \Omega\) resistors in series. An ammeter of internal resistance \(0.50 \Omega\) measures the current, and at the same time a voltmeter with internal resistance \(15 \mathrm{k} \Omega\) measures the voltage across one of the \(9.0-\mathrm{k} \Omega\) resistors in the circuit. What do the ammeter and voltmeter read?

(III) What internal resistance should the voltmeter of Example19-15 have to be in error by less than 3%?

(III) When the resistor R in Fig. 19-59 is \(35 \Omega\), the high-resistance voltmeter reads 9.7 V. When R is replaced by a \(9.0-\Omega\) resistor, the voltmeter reading drops to 8.1 V. What Are the emf and internal resistance of the battery?

Problem 64GP Suppose that you wish to apply a 0.25-V potential difference between two points on the human body. The resistance is about 2000 ?, and you only have a 9.0-V battery. How can you connect up one or more resistors to produce the desired voltage?

Problem 66GP Suppose you want to run some apparatus that is 95 m from an electric outlet. Each of the wires connecting your apparatus to the 120-V source has a resistance per unit length of 0.0065 ?/m. If your apparatus draws 3.0 A, what will be the voltage drop across the connecting wires and what voltage will be applied to your apparatus?

Electricity can be a hazard in hospitals, particularly to patients who are connected to electrodes, such as an ECG. For example, 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, she 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. 19-60. Calculate the current through the patient. FIGURE 19-60 Problem 67.

Problem 69GP A heart pacemaker is designed to operate at 72 beats/min using a 7.5-?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 63% of maximum?

How much energy must a 45-V battery expend to charge a \(0.40-\mu F\) and a \(0.60-\mu F\) capacitor fully when they are placed (a) in parallel, (b) in series? (c) How much charge flowed from the battery in each case?

Problem 70GP Suppose that a person’s body resistance is 950 ?. (a) What current passes through the body when the person accidentally is connected to 110 V? (b) If there is an alternative path to ground whose resistance is 45 ?, what current passes through the person? (c) If the voltage source can produce at most 1.5 A, how much current passes through the person in case (b)?

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. 19-61). One of these, \(R_3\), is a variable resistor which is adjusted so that when the switch is closed momentarily, the ammeter (A) shows zero current flow. (a) Determine \(R_X\) in terms of \(R_1, R_2\), and \(R_3\). (b) If a Wheatstone bridge is "balanced" when \(R_1=630 \Omega, R_2=972 \Omega\), and \(R_3=42.6 \Omega\), what is the value of the unknown resistance?

How many \(\frac{1}{2}-W\) resistors, each of the same resistance, must be used to produce an equivalent \(2.2-k \Omega, 3.5-W\) 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 2.2-k \Omega, 3.5-W P=\frac{1}{2} W

The variable capacitance of an old radio tuner consists of four plates connected together placed alternately between four other plates, also connected together (Fig. 19-62). Each plate is separated from its neighbor by \(1.5 \mathrm{~mm}\) of air. One set of plates can move so that the area of overlap of each plate varies from \(2.0 \mathrm{~cm}^{2}$ to $9.5 \mathrm{~cm}^{2}\) (a) Are these seven capacitors connected in series or in parallel? Determine the range of capacitance values. FIGURE 19-62 Problem 74 Equation Transcription: Text Transcription: 1.5 mm 2.0 cm2 to 9.5 cm2

An unknown length of platinum wire \(0.920 \mathrm{~mm}\) in diameter is placed as the unknown resistance in a Wheatstone bridge (see Problem 71; Fig, ). Arms 1 and 2 have resistance of \(38.0 \Omega\) and \(46.0 \Omega\), respectively. Balance is achieved when \(R_{2} is 3.48 \Omega\). How long is the platinum wire? FIGURE 19-61 Problem 71 and 72. Wheatstone bridge. Equation Transcription: Text Transcription: 0.920 mm 38.0 \Omega 46.0 \Omega R2 is 3.48 \Omega

The current through the \(4.0-k \Omega\) resistor in Fig. is \(3.50 \mathrm{~mA}\). What is the terminal voltage \(V_{b a}\) of the "unknown" battery? (There are two answers. Why?) [Hint: use conservation of energy or Kirchhoff's rules.] FIGURE 19-63 Problem 77 Equation Transcription: Text Transcription: 4.0-k\Omega 3.50 mA Vba

An air-filled parallel-plate capacitor has capacitance \(C_0\). If two identically sized dielectric slabs of dielectric constants \(K_1\) and \(K_2\) are inserted as shown in Fig. 19-64, what is the new capacitance? [Hint: treat this as two capacitors in combination.]

For the circuit shown in Fig. 19-65, determine (a) the current through the \(14-\mathrm{V}\) battery and (b) the potential difference between points a and \(\mathrm{b}, V_{\mathrm{a}}-V_{\mathrm{b}}\).

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 1.0 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? How can you optimize the output of your solar panel?

A power supply has a fixed output voltage of \(12.0 \mathrm{~V}\), but you need \(V_{\mathrm{T}}=3.0 \mathrm{~V}\) for an experiment. (a) Using the voltage divider shown in Fig. 19-66, what should \(R_2\) be if \(R_1\) is \(10.0 \Omega\) ? (b) What will the terminal voltage \(V_{\mathrm{T}}\) be if you connect a load to the \(3.0-\mathrm{V}\) terminal, assuming the load has a resistance of \(7.0 \Omega\) ?

In the circuit shown in Fig. 19-69, the \(33-\Omega\) resistor dissipates 0.50 W. What is the battery voltage?

(a) What is the equivalent resistance of the circuit shown in Fig. What is the current in the \(18-\Omega\) resistor? (c) What is the current in the \(12-\Omega\) resistor? What is the power dissipation in the \(4.5-\Omega\) resistor? FIGURE 19-70 Problem 85. Equation Transcription: Text Transcription: 18-\Omega 12-\Omega 4.5-\Omega

A flashlight bulb rated at \(2.5 \mathrm{~W} \text { and } 3.0 \mathrm{~V}\) is operated by a \(9.0-\mathrm{V}\) battery. To light the bulb at its rated voltage and power, a resistor is connected in series as shown in Fig. . What value should the resistor have? FIGURE 19-72 Problem 87. Equation Transcription: Text Transcription: 2.5 W and 3.0 V 9.0-V