Highly sensitive ammeters can measure currents as small as

Problem 131IP IP Referring to Example 21-9 Suppose the capacitance of the 182-?F capacitor is reduced by a factor of 2. The two resistors are 126 ? and 275 ?, and the battery has an emf of 3.00 V. (a) Find the final value of the charge on the capacitor, (b) Does the time for the capacitor to charge to 80.0% of its final value increase, decrease, or stay the same? Explain, (c) Find the time referred to in part (b).

Problem 2CQ Your body is composed of electric charges. Does it follow, then, that you produce an electric current when you walk?

Problem 1CQ What is the direction of the electric current produced by an electron that falls toward the ground?

Problem 1P How many coulombs of charge are in one ampere-hour?

Problem 3CQ Suppose you charge a comb by rubbing it through your hair. Do you produce a current when you walk across the room carrying the comb?

Problem 2P A flashlight bulb carries a current of 0.18 A for 78 s. How much charge flows through the bulb in this time? How many electrons?

Problem 4CQ Suppose you charge a comb by rubbing it through the fur on your dog's back. Do you produce a current when you walk across the room carrying the comb?

Problem 3P The picture tube in a particular television draws a current of 15 A. How many electrons strike the viewing screen every second?

Problem 4P IP A car battery does 260 J of work on the charge passing through it as it starts an engine, (a) If the emf of the battery is 12V, how much charge passes through the battery during the start? (b) If the emf is doubled to 24 V, does the amount of charge passing through the battery increase or decrease? By what factor?

Problem 5P Highly sensitive ammeters can measure currents as small as 10.0 fA. How many electrons per second flow through a wire with a 10.0-fA current?

Problem 5CQ An electron moving through a wire has an average drift speed that is very small. Does this mean that its instantaneous velocity is also very small?

Problem 6CQ Arc car headlights connected in series or parallel? Give an everyday observation that supports your answer.

Problem 6P A television set connected to a 120-V outlet consumes 78 W of power, (a) How much current flows through the television? (b) How long does it take for 10 million electrons to pass through the TV?

Problem 7CQ Give an example of how four resistors of resistance R can be combined to produce an equivalent resistance of R.

Problem 7P BIO Pacemaker Batteries Pacemakers designed for long term use commonly employ a lithium-iodine battery capable of supplying 0.42 A · h of charge, (a) How many coulombs of charge can such a battery supply? (b) If the average current produced by the pacemaker is 5.6 ? A, what is the expected lifetime of the device?

Problem 9CQ What physical quantity do resistors connected in series have in common?

Problem 8P CE A conducting wire is quadrupled in length and tripled in diameter, (a) Does its resistance increase, decrease, or stay the same? Explain, (b) By what factor does its resistance change?

Figure 21–26 shows a plot of current versus voltage for two different materials, A and B. Which of these materials satisfies Ohm’s law? Explain.

Problem 8CQ Is it possible to connect a group of resistors of value R in such a way that the equivalent resistance is less than R? If so, give a specific example.

Problem 10CQ What physical quantity do resistors connected in parallel have in common?

Current-versus-voltage plots for two materials, A and B, are shown in Figure 21–26. (a) Is the resistance of material A greater than, less than, or equal to the resistance of material B at the voltage \(V_{1}\)? (b) Choose the best explanation from among the following: 1. Curve B is higher in value than curve A. 2. A larger slope means a larger value of I/V , and hence a smaller value of R. 3. Curve B has the larger slope at the voltage and hence the larger resistance. Equation Transcription: Text Transcription: V_1

Problem 11CQ Explain how electrical devices can begin operating almost immediately after you throw a switch, even though individual electrons in the wire may take hours to reach the device.

Problem 11P Two cylindrical wires are made of the same material and have the same length. If wire B is to have nine times the resistance of wire A, what must be the ratio of their radii, rB/rA?

Problem 12CQ Explain the difference between resistivity and resistance.

Problem 13CQ Explain why birds can roost on high-voltage wire without being electrocuted.

Problem 12P A silver wire is 5.9 m long and 0.49 mm in diameter. What is its resistance?

Problem 13P When a potential difference of 18 V is applied to a given wire, it conducts 0.35 A of current. What is the resistance of the wire?

Problem 14CQ List two electrical applications that would benefit from room-temperature superconductors. List two applications for which room-temperature superconductivity would not be beneficial.

Problem 15CQ Oil what basic conservation laws are Kirchhoff's rules based 7

Problem 15P What is the resistance of 6.0 mi of copper wire with a diameter of 0.55 mm?

Problem 16CQ What physical quantity do capacitors connected in series have in common?

The four conducting cylinders shown in Figure 21–27 are all made of the same material, though they differ in length and/or diameter. They are connected to four different batteries, which supply the necessary voltages to give the circuits the same current, I. Rank the four voltages, \(V_{1}=V_{2}, V_{3}, \text { and } V_{4}\), in order of increasing value. Indicate ties where appropriate. Equation Transcription: Text Transcription: V_{1}=V_{2}, V_{3}, \text { and } V_{4}

Problem 17CQ What physical quantity do capacitors connected in parallel have in common?

Problem 17P IP A bird lands on a bare copper wire carrying a current of 32 A. The wire is 8 gauge, which means that its cross-sectional area is 0.13 cm2, (a) Find the difference in potential between the bird's feet, assuming they are separated by a distance of 6.0 cm. (b) Will your answer to part (a) increase or decrease if the separation between the bird's feet increases? Explain.

Consider the circuit shown in Figure 21–25, in which a light of resistance R and a capacitor of capacitance C are connected in series. The capacitor has a large capacitance, and is initially uncharged. The battery provides enough power to light the bulb when connected to the battery directly. Describe the behavior of the light after the switch is closed.

Problem 18P A current of 0.96 A flows through a copper wire 0.44 mm in diameter when it is connected to a potential difference of 15 V. How long is the wire?

Problem 19P IP BIO Current Through a Cell Membrane A typical cell membrane is 8.0 nm thick and has an electrical resistivity of 1.3 × 107 ? · m. (a) If the potential difference between the inner and outer surfaces of a cell membrane is 75 mV, how much current flows through a square area of membrane 1.0 ? m on a side? (b) Suppose the thickness of the membrane is doubled, but the resistivity and potential difference remain the same. Does the current increase or decrease? By what factor?

Problem 24P CE Light A has four times the power rating of light B when operated at the same voltage, (a) Is the resistance of light A greater than, less than, or equal to the resistance of light B? Explain, (b) What is the ratio of the resistance of light A to the resistance of light B?

Problem 25P CE Two light bulbs operate on the same potential difference. Bulb A has four times the power output of bulb B. (a) Which bulb has the greater current passing through it? Explain, (b) What is the ratio of the current in bulb A to the current in bulb B?

Problem 20P When a potential difference of 12 V is applied to a wire 6.9 m long and 0.33 mm in diameter, the result is an electric current of 2.1 A. What is the resistivity of the wire?

Problem 22P BIO Resistance and Current in the Human Finger The interior of the human body has an electrical resistivity of 0.15 ? · m. (a) Estimate the resistance for current flowing the length of your index finger. (For this calculation, ignore the much higher resistivity of your skin.) (b) Your muscles will contract when they carry a current greater than 15 mA. What voltage is required to produce this current through your finger?

Consider a rectangular block of metal of height A, width B, and length C, as shown in Figure 21–28. If a potential difference V is maintained between the two \(A X B \) faces of the block, a current \(I_{A B}\) is observed to flow. Find the current that flows if the same potential difference V is applied between the two \(B X C\) faces of the block. Give your answer in terms of \(I_{A B}\). Equation Transcription: Text Transcription: A X B IAB B X C IAB

Problem 21P IP (a) What is the resistance per meter of an aluminum wire with a cross-sectional area of 2.4 × 10-7 m2. (b) Would your answer to part (a) increase, decrease, or stay the same if the diameter of the wire were increased? Explain, (c) Repeat part (a) for a wire with a cross-sectional area of 3.6 × 10?7 m2.

Problem 26P CE Two light bulbs operate on the same current. Bulb A has four times the power output of bulb B. (a) Is the potential difference across bulb A greater than or less than the potential difference across bulb B? Explain, (b) What is the ratio of the potential difference across bulb A to that across bulb B?

Problem 28P A portable CD player operates with a current of 22 mA at a potential difference of 4.1 V. What is the power usage of the player?

Problem 27P A 75-V generator supplies 3.8 kW of power. How much current does the generator produce?

Problem 29P Find the power dissipated in a 25-? electric heater connected to a 120-V outlet.

Problem 30P The current in a 120-V reading lamp is 2.6 A. If the cost of electrical energy is $0.075 per kilowatt-hour, how much does it cost to operate the light for

Problem 31P It costs 2.6 cents to charge a car battery at a voltage of 12 V and a current of 15 A for 120 minutes. What is the cost of electrical energy per kilowatt-hour at this location?

Problem 34P CE Predict/Explain A dozen identical lightbulbs are connected to a given emf. (a) Will the lights be brighter if they are connected in series or in parallel? (b) Choose the best explanation from among the following: I. When connected in parallel each bulb experiences the maximum emf and dissipates the maximum power. II. Resistors in series have a larger equivalent resistance and dissipate more power. III. Resistors in parallel have a smaller equivalent resistance and dissipate less power.

Problem 32P IP A 75-W lightbulb operates on a potential difference of 95 V. Find (a) the current in the bulb and (b) the resistance of the bulb, (c) If this bulb is replaced with one whose resistance is half the value found in part (b), is its power rating greater than or less than 75 W? By what factor?

Problem 33P Rating Car Batteries Car batteries are rated by the following two numbers: (1) cranking amps = current the battery can produce for 30.0 seconds while maintaining a terminal voltage of at least 7.2 V and (2) reserve capacity = number of minutes the battery can produce a 25-A current while maintaining a terminal voltage of at least 10.5 V. One particular battery is advertised as having 905 cranking amps and a 155-minute reserve capacity. Which of these two ratings represents the greater amount of energy delivered by the battery?

Problem 35P CE Predict/Explain A fuse is a device to protect a circuit from the effects of a large current. The fuse is a small strip of metal that burns through when the current in it exceeds a certain value, thus producing an open circuit, (a) Should a fuse be connected in series or in parallel with the circuit it is intended to protect? (b) Choose the best explanation from among the following: I. Either connection is acceptable; the main tiling is to have a fuse in the circuit. II. The fuse should be connected in parallel, otherwise it will interrupt the current in the circuit. III. With the fuse connected in series, the current in the circuit drops to zero as soon as the fuse bruns through.

Problem 36P CE A circuit consists of three resistors, R123, connected in series to a battery. Rank these resistors in order of increasing (a) current through them and (b) potential difference across them. Indicate ties where appropriate.

Find the equivalent resistance between points A and B for the group of resistors shown in Figure 21–29.

Problem 39P What is the minimum number of 65-? resistors that must be connected in parallel to produce an equivalent resistance of 11 ? or less?

Problem 37P CE Predict/Explain Two resistors are connected in parallel, (a) If a third resistor is now connected in parallel with the original two, does the equivalent resistance of the circuit increase, decrease, or remain the same? (b) Choose the best explanation from among the following: I. Adding a resistor generally tends to increase the resistance, but putting it in parallel tends to decrease the resistance; therefore the effects offset and the resistance stays the same. II. Adding more resistance to the circuit will increase the equivalent resistance. III. The third resistor gives yet another path for current to flow in the circuit, which means that the equivalent resistance is less.

Four lightbulbs (A, B, C, D) are connected together in a circuit of unknown arrangement. When each bulb is removed one at a time and replaced, the following behavior is observed: Draw a circuit diagram for these bulbs.

Problem 41P Your toaster has a power cord with a resistance of 0.020 ? connected in series with a 9.6-? nichrome heating element. If the potential difference between the terminals of the toaster is 120 V, how much power is dissipated in (a) the power cord and (b) the heating element?

Problem 43P A circuit consists of a 12.0-V battery connected to three resistors (42 ?, 17 ?, and 110 ?) in series. Find (a) the current that flows through the battery and (b) the potential difference across each resistor.

Problem 42P A hobbyist building a radio needs a 150-? resistor in her circuit, but has only a 220-?, a 79-?, and a 92-? resistor available. How can she connect these resistors to produce the desired resistance?

Problem 45P A circuit consists of a battery connected to three resistors (65 ?, 25 ?, and 170 ?) in parallel. The total current through the resistors is 1.8 A. Find (a) the emf of the battery and (b) the current through each resistor.

Problem 47P An 89-? resistor has a current of 0.72 A and is connected in series with a 130-? resistor. What is the emf of the battery to which the resistors are connected?

Problem 46P IP Three resistors, 22 ?, 67 ?, and R, are connected in parallel with a 12.0-V battery. The total current flowing through the battery is 0.88 A. (a) Find the value of resistance R. (b) Find the current through each resistor, (c) If the total current in the battery had been greater than 0.88 A, would your answer to part (a) have been larger or smaller? Explain.

Problem 44P IP Three resistors, 11 ?, 53 ?, and R, are connected in series with a 24.0-V battery. The total current flowing through the battery is 0.16 A. (a) Find the value of resistance R. (b) Find the potential difference across each resistor, (c) If the voltage of the battery had been greater than 24.0 V, would your answer to part (a) have been larger or smaller? Explain.

The equivalent resistance between points A and B of the resistors shown in Figure 21–30 is \(26 \Omega\). Find the value of resistance R. Equation Transcription: Text Transcription: 26 \Omega

Find the equivalent resistance between points A and B shown in Figure 21–31. Equation Transcription: Text Transcription: 4.8 \Omega 3.3 \Omega 1.5 \Omega 2.5 \Omega 8.1 \Omega 6.3 \Omega

Problem 50P How many 65-W light bulbs can be connected m parallel across a potential difference of 85 V before the total current in the circuit exceeds 2.1 A?

The circuit in Figure 21–32 includes a battery with a finite internal resistance, \(r=0.50 \Omega\). (a) Find the current flowing through the \(7.1-\Omega\) and the \(3.2-\Omega\) resistors. (b) How much current flows through the battery? (c) What is the potential difference between the terminals of the battery? Equation Transcription: Text Transcription: r=0.50 \Omega 7.1 - \Omega 3.2-\Omega 1.0 \Omega 4.5 \Omega 5.8 \Omega r 12.0 V ________________

The terminals A and B in Figure 21–31 are connected to a 9.0-V battery. (a) Find the current flowing through each resistor. (b) Is the potential difference across the \(6.3-\Omega\) resistor greater than, less than, or the same as the potential difference across the \(1.5-\Omega\) resistor? Explain. Equation Transcription: Text Transcription: 6.3-\Omega 1.5-\Omega

A 12-V battery is connected to terminals A and B in Figure 21–30. (a) Given that \(R=85 \Omega\), find the current in each resistor. (b) Suppose the value of R is increased. For each resistor in turn, state whether the current flowing through it increases or decreases. Explain. Equation Transcription: Text Transcription: R=85 \Omega

Suppose the battery in Figure 21–32 has an internal resistance \(r=0.25 \Omega\). (a) How much current flows through the battery? (b) What is the potential difference between the terminals of the battery? (c) If the \(3.2-\Omega\) resistor is increased in value, will the current in the battery increase or decrease? Explain. Equation Transcription: Text Transcription: r=0.25 \Omega 3.2-\Omega

The current flowing through the \(8.45-\Omega\) resistor in Figure 21–33 is 1.52 A. (a) What is the voltage of the battery? (b) If the \(17.2-\Omega\) resistor is increased in value, will the current provided by the battery increase, decrease, or stay the same? Explain. Equation Transcription: Text Transcription: 8.45-\Omega 17.2-\Omega

The current in the \(13.8-\Omega\) resistor in Figure 21–33 is 0.795 A. Find the current in the other resistors in the circuit. Equation Transcription: Text Transcription: 13.8-\Omega 12.5 \Omega 8.45 \Omega 13.8 \Omega 17.2 \Omega 15.0 \Omega 4.11 \Omega

Find the magnitude and direction (clockwise or counterclockwise) of the current in Figure 21–35. Equation Transcription: Text Transcription: 8.50 \Omega 11.5 V 15.0 V 6.22 \Omega 15.1 \Omega

Suppose point A is grounded in \((V=0)\) in Figure 21–36. Find the potential at points B and C. Equation Transcription: Text Transcription: (V=0) 6.2 \Omega 15 V 7.5 \Omega 12 \Omega 11 \Omega

Four identical resistors are connected to a battery as shown in Figure 21–34. When the switch is open, the current through the battery is \(I_{0}\). (a) When the switch is closed, will the current through the battery increase, decrease, or stay the same? Explain. (b) Calculate the current that flows through the battery when the switch is closed. Give your answer in terms of \(I_{0}\).. Equation Transcription: Text Transcription: I_{0} I_{0}

(a) Find the current in each resistor in Figure 21–37. (b) Is the potential at point A greater than, less than, or equal to the potential at point B? Explain. (c) Determine the potential difference between the points A and B. Equation Transcription: Text Transcription: 3.9 \Omega 6.7 \Omega 12 V 1.2 \Omega 9.0 V 9.8 \Omega

It is given that point A in Figure 21–35 is grounded (V = 0). (a) Is the potential at point B greater than or less than zero? Explain. (b) Is the potential at point C greater than or less than zero? Explain. (c) Calculate the potential at point D. Equation Transcription: Text Transcription: (V=0) ________________

Suppose the polarity of the 11.5-V battery in Figure 21–35 is reversed. (a) Do you expect this to increase or decrease the amount of current flowing in the circuit? Explain. (b) Calculate the magnitude and direction (clockwise or counterclockwise) of the current in this case.

Consider the circuit shown in Figure 21–36. Find the current through each resistor using (a) the rules for series and parallel resistors and (b) Kirchhoff’s rules. Equation Transcription: Text Transcription: 6.2 \Omega 15 V 7.5 \Omega 12 \Omega 11 \Omega

Problem 67P CE Predict/Explain Two capacitors are connected in parallel, (a) If a third capacitor is now connected in parallel with the original two, does the equivalent capacitance increase, decrease, or remain the same? (b) Choose the best explanation from among the following: I. Adding a capacitor tends to increase the capacitance, but putting it in parallel tends to decrease the capacitance; therefore, the net result is no change. II. Adding a capacitor in parallel will increase the total amount of charge stored, and hence increase the equivalent capacitance. III. Adding a capacitor in parallel decreases the equivalent capacitance since each capacitor now has less voltage across it, and hence stores less charge.

Problem 66P CE Predict/Explain Two capacitors are connected in series, (a) If a third capacitor is now connected in series with the original two, does the equivalent capacitance increase, decrease, or remain the same? (b) Choose the best explanation from among the following: I. Adding a capacitor generally tends to increase the capacitance, but putting it in series tends to decrease the capacitance; therefore, the net result is no change. II. Adding a capacitor in series will increase the total amount of charge stored, and hence increase the equivalent capacitance. III. Adding a capacitor in series decreases the equivalent capacitance since each capacitor now has less voltage across it, and hence stores less charge.

Find the equivalent capacitance between points A and B for the group of capacitors shown in Figure 21–39. Equation Transcription: Text Transcription: 15 \mu F 8.2 \mu F 22 \mu F

Two batteries and three resistors are connected as shown in Figure 21–38. How much current flows through each battery when the switch is (a) closed and (b) open? Equation Transcription: Text Transcription: 6.0 V 9.0 V 2.0 \Omega 4.0 \Omega 5.0 \Omega

Problem 69P A 12-V battery is connected to three capacitors in series. The capacitors have the following capacitances: 4.5 ? F, 12 ? F, and 32 ? F. Find the voltage across the 32- ? F capacitor.

Problem 65P CE Two capacitors, C1 = C and C2 = 2C, are connected to a battery, (a) Which capacitor stores more energy when they are connected to the battery in series? Explain, (b) Which capacitor stores more energy when they are connected in parallel? Explain.

The equivalent capacitance of the capacitors shown in Figure 21–41 is 9.22 ?F. Find the value of capacitance C. Equation Transcription: Text Transcription: 9.22 \mu F 12.0 \mu F 7.22 \mu F 4.25 \mu F 8.35 \mu F

Problem 70P CE You conduct a series of experiments in which you connect the capacitors C1 and C2 > C1 to a battery in various ways. The experiments are as follows: A, C1 alone connected to the battery; B, C2 alone connected to the battery; C, C1 and C2 connected to the battery in series; D, C1 and C2 connected to the battery in parallel. Rank these four experiments in order of increasing equivalent capacitance. Indicate ties where appropriate.

Problem 72P Terminals A and B in Figure 21-39 are connected to a 9.0-V battery. Find the energy stored in each capacitor.

Problem 74P IP Two capacitors, one 7.5 ? F and the other 15 ? F, are connected in series across a 15-V battery, (a) Find the equivalent capacitance of the two capacitors, (b) Which capacitor stores more charge? Explain, (c) Find the charge stored on each capacitor.

Three different circuits, each containing a switch and two capacitors, are shown in Figure 21–40. Initially, the plates of the capacitors are charged as shown. The switches are then closed, allowing charge to move freely between the capacitors. Rank the circuits in order of increasing final charge on the left plate of (a) the upper capacitor and (b) the lower capacitor. Indicate ties where appropriate.

Problem 73P IP Two capacitors, one 7.5 ? F and the other 15 ? F, are connected in parallel across a 15-V battery, (a) Find the equivalent capacitance of the two capacitors, (b) Which capacitor stores more charge? Explain, (c) Find the charge stored on each capacitor.

Problem 76P Two capacitors, C1 and C2, are connected in series and charged by a battery. Show that the energy stored in C1 plus the energy stored in C2 is equal to the energy stored in the equivalent capacitor, Ceq, when it is connected to the same battery.

With the switch in position A, the \(11.2 \mu F\) capacitor in Figure 21–42 is fully charged by the \(12.0-V\) battery, and the \(9.50-\mu F\) capacitor is uncharged. The switch is now moved to position B. As a result, charge flows between the capacitors until they have the same voltage across their plates. Find this voltage. Equation Transcription: Text Transcription: 11.2 \mu F 12.0-V 9.50- \mu F

Problem 79P ? The capacitor in an RC circuit (R = 120 ?, C = 45 ? F) is initially uncharged. Find (a) the charge on the capacitor and (b) the current in the circuit one time constant (? = RC) after the circuit is connected to a 9.0-V battery.

Problem 78P The switch on an RC circuit is closed at t = 0. Given that ? = 9.0 V, R = 150 ?, and C = 23 ? F, how much charge is on the capacitor at time t = 4.2 ms?

Problem 81P Consider an RC circuit with ? = 12.0 V, R = 175 ?, and C = 55.7 ? F. Find (a) the time constant for the circuit, (b) the maximum charge on the capacitor, and (c) the initial current in the circuit.

Three RC circuits have the emf, resistance, and capacitance given in the accompanying table. Initially, the switch on the circuit is open and the capacitor is uncharged. Rank these circuits in order of increasing (a) initial current (immediately after the switch is closed) and (b) time for the capacitor to acquire half its final charge. Indicate ties where appropriate.

Problem 82P The resistor in an RC circuit has a resistance of 145 ?. (a) What capacitance must be used in this circuit if the time constant is to be 3.5 ms? (b) Using the capacitance determined in part (a), calculate the current in the circuit 7.0 ms after the switch is closed. Assume that the capacitor is uncharged initially and that the emf of the battery is 9.0 V.

Problem 88GP CE? ?Predict/Explain? The resistivity of tungsten increases with temperature, (a) When a light containing a tungsten filament heats up, does its power consumption increase, decrease, or stay the same? (b)? Choose the best explanation from among the following: I?. The voltage is unchanged, and therefore an increase in resistance implies a reduced power, as we can see from P = V2/R. II. Increasing the resistance increases the power, as is clear from P = I2R. III. The power consumption is independent of resistance, as we can see from P = IV.

Problem 83P A flash unit for a camera has a capacitance of 1500 ? F. What resistance is needed in this RC circuit if the flash is to charge to 90% of its full charge in 21 s?

Consider the RC circuit shown in Figure 21–44. Find (a) the time constant and (b) the initial current for this circuit. (c) It is desired to increase the time constant of this circuit by adjusting the value of the \(6.5-\Omega\) resistor. Should the resistance of this resistor be increased or decreased to have the desired effect? Explain. Equation Transcription: Text Transcription: 6.5- \Omega 6.5 \Omega 13 \Omega 24 \Omega 62 \mu F 15 V

Figure 21–43 shows a simplified circuit for a photographic flash unit. This circuit consists of a \(9.0-V\) battery, a \(50.0-k \Omega\) resistor, a \(140-\mu F\) capacitor, a flashbulb, and two switches. Initially, the capacitor is uncharged and the two switches are open. To charge the unit, switch \(S_{1}\) is closed; to fire the flash, switch \(S_{2}\) (which is connected to the camera’s shutter) is closed. How long does it take to charge the capacitor to \(5.0 V\)? Equation Transcription: Text Transcription: 9.0-V 50.0-k \Omega 140- \mu F S1 S2 5.0 V

Problem 86P The capacitor in an RC circuit is initially uncharged. In terms of R and C, determine (a) the time required for the charge on the capacitor to rise to 50% of its final value and (b) the time required for the initial current to drop to 10% of its initial value.

Problem 87GP CE A given car battery is rated as 250 amp-hours. Is this rating a measure of energy, power, charge, voltage, or current? Explain.

(a) Referring to Problem 92 and the circuit in Figure 21–45, does the current supplied by the battery increase, decrease, or remain the same when the switch is closed? (b) Choose the best explanation from among the following: I. The current decreases because only two resistors can draw current from the battery when the switch is closed. II. Closing the switch makes no difference to the current since the second resistor is still connected to the battery as before. III. Closing the switch shorts out the second resistor, decreases the total resistance of the circuit, and increases the current.

(a) Referring to Problem 92 and the circuit in Figure 21–45, does the total power dissipated in the circuit increase, decrease, or remain the same when the switch is closed? (b) Choose the best explanation from among the following: I. Closing the switch shorts out one of the resistors, which means that the power dissipated decreases. II. The equivalent resistance of the circuit is reduced by closing the switch, but the voltage remains the same. Therefore, from \(P-V^{2} / R\) we see that the power dissipated increases. III. The power dissipated remains the same because power, \(P=I V\), is independent of resistance. Equation Transcription: Text Transcription: P-V2/R P=IV

(a) When the switch is closed in the circuit shown in Figure 21–46, does the current supplied by the battery increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The current increases because three resistors are drawing current from the battery when the switch is closed, rather than just two. II. Closing the switch makes no difference to the current because the voltage is the same as before. III. Closing the switch decreases the current because an additional resistor is added to the circuit.

(a) When the switch is closed in the circuit shown in Figure 21–46, does the total power dissipated in the circuit increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. Closing the switch adds one more resistor to the circuit. This makes it harder for the battery to supply current, which decreases the power dissipated. II. The equivalent resistance of the circuit is reduced by closing the switch, but the voltage remains the same. Therefore, from \(P=V^{2} / R\) we see that the power dissipated increases. III. The power dissipated remains the same because power, \(P=I V\), is independent of resistance. Equation Transcription: Text Transcription: P=V2/R P=IV

Consider the circuit shown in Figure 21–46, in which three lights, each with a resistance R, are connected in parallel. The circuit also contains an open switch. (a) When the switch is closed, does the intensity of light 3 increase, decrease, or stay the same? Explain. (b) Do the intensities of lights 1 and 2 increase, decrease, or stay the same when the switch is closed? Explain.

Problem 89GP CE A cylindrical wire is to be doubled in length, but it is desired that its resistance remain the same, (a) Must its radius be increased or decreased? Explain, (b) By what factor must the radius be changed?

Suppose that points A and B in Figure 21–30 are connected to a \(12-V\) battery. Find the power dissipated in each of the resistors assuming that \(R=65 \Omega\) Equation Transcription: Text Transcription: 12-V R=65 \Omega 12 \Omega 55 \Omega

Problem 99GP You are given resistors of 413 ?, 521 ?, and 146 ?. Describe how these resistors must be connected to produce an equivalent resistance of 255 ?.

Problem 100GP You arc given capacitors of 18 ?F, 7.2 ?F, and 9.0 ?F. Describe how these capacitors must be connected to produce an equivalent capacitance of 22 ?F.

Problem 112GP BIO Pacemaker Pulses A pacemaker sends a pulse to a patient's heart every time the capacitor in the pacemaker charges to a voltage of 0.25 V. It is desired that the patient receive 75 pulses per minute. Given that the capacitance of the pacemaker is 110 ?F and that the battery has a voltage of 9.0 V, what value should the resistance have?

Problem 113GP A long, thin wire has a resistance R. The wire is now cut into three segments of equal length, which are connected in parallel. In terms of R, what is the equivalent resistance of the three wire segments?

Suppose we connect a 12.0-V battery to terminals A and B in Figure 21–29. (a) Is the current in the \(45-\Omega\) resistor greater than, less than, or the same as the current in the \(35-\Omega) resistor? Explain. (b) Calculate the current flowing through each of the three resistors in this circuit. Equation Transcription: Text Transcription: 45- \Omega 35- \Omega 82 \Omega

Problem 116GP IP Suppose the battery in Figure 21-50 has an internal resistance of 0.73 ?. (a) What is the potential difference across the terminals of the battery when the switch is open? (b) When the switch is closed, does the potential difference of the battery increase or decrease? Explain, (c) Find the potential difference across the battery after the switch has been closed a long time.

Three resistors \(\left(R, \frac{1}{2} R, 2 R\right)\) are connected to a battery. (a) If the resistors are connected in series, which one has the greatest rate of energy dissipation? (b) Repeat part (a), this time assuming that the resistors are connected in parallel. Equation Transcription: Text Transcription: (R, \frac{1}{2} R, 2 R)

Problem 108GP An electrical heating coil is immersed in 4.6 kg of water at 22 °C. The coil, which has a resistance of 250 ?, warms the water to 32 °C in 15 min. What is the potential difference at which the coil operates?

Consider the circuit shown in Figure 21–50. (a) Is the current flowing through the battery immediately after the switch is closed greater than, less than, or the same as the current flowing through the battery long after the switch is closed? Explain. (b) Find the current flowing through the battery immediately after the switch is closed. (c) Find the current in the battery long after the switch is closed. Equation Transcription: Text Transcription: 45 \mu F 11 \Omega 5.6 \Omega 9.0 V

National Electric Code In the United States, the National Electric Code sets standards for maximum safe currents in insulated copper wires of various diameters. The accompanying table gives a portion of the code. Notice that wire diameters are identified by the gauge of the wire, and that \(1 \mathrm{mil}=10^{-3}\) in. Find the maximum power dissipated per length in (a) an 8-gauge wire and (b) a 10-gauge wire. Equation Transcription: Text Transcription: 1 mil=10-3

Problem 118GP IP 15.0-V battery is connected to terminals A and B in Figure 21-41. (a) Given that C = 15.0 ?F, find the charge on each of the capacitors, (b) Find the total energy stored in this system, (c) If the 7.22-?F capacitor is increased in value, will the total energy stored in the circuit increase or decrease? Explain.

Problem 120GP Two resistors, R1 and R2, are connected in parallel and connected to a battery. Show that the power dissipated in R1 plus the power dissipated in R2 is equal to the power dissipated in the equivalent resistor, Req, when it is connected to the same battery.

Problem 122GP When two resistors, R1 and R2, are connected in series across a 6.0-V battery, the potential difference across R1 is 4.0 V. When R1 and R2 are connected in parallel to the same battery, the current through R2 is 0.45 A. Find the values of R1 and R2.

Problem 121GP A battery has an emf ? and an internal resistance r. When the battery is connected to a 25-? resistor, the current through the battery is 0.65 A. When the battery is connected to a 55-? resistor, the current is 0.45 A. Find the battery's emf and internal resistance.

The circuit shown in Figure 21–51 is known as a Wheatstone bridge. Find the value of the resistor R such that the current through the \(85.0-\Omega\) resistor is zero. Equation Transcription: Text Transcription: 85.0-\Omega 25.0 \Omega 15.0 \Omega 15.0 V 85.0 \Omega 12.5 \Omega

Problem 119GP IP The switch in the RC circuit shown in Figure 21-44 is closed at t = 0. (a) How much power is dissipated in each resistor just after t = 0 and in the limit t ? ?? (b) What is the charge on the capacitor at the time t = 0.35 ms? (c) How much energy is stored in the capacitor in the limit t ? ??? (d) If the voltage of the battery is doubled, by what factor does your answer to part (c) change? Explain.

Problem 124PP Suppose the voltmeter measures a potential difference of 3.70 V across the resistor. What is the current that flows through the person's body? A. 3.70 × 10-6A B. 5.00 × 10-5A C. 0.0740 A D. 3.70 A

Problem 125PP What is the resistance of the person and footwear when the voltmeter reads 3.70 V? A. 1.25 × 107? B. 1.35 × 107 ? C. 4.63 × 107 ? D. 1.71 × 108 ?

Problem 126PP The resistance of a given person and footwear is 4.00 × 107? What is the reading on the voltmeter when this person is tested? A. 0.976 V B. 1.22 V C. 1.25 V D. 50.0 V

Problem 127PP Suppose that during one test a person's shoes become wet when water spills onto the floor. When this happens, do you expect the reading on the voltmeter to increase, decrease, or stay the same?

Problem 130IP IP Referring to Example 21-9 Suppose the resistance of the 126-? resistor is reduced by a factor of 2. The other resistor is 275 ?, the capacitor is 182 ?F, and the battery has an emf of 3.00 V. (a) Does the filial value of the charge on the capacitor increase, decrease, or stay the same? Explain, (b) Does the time for the capacitor to charge to 80.0% of its final value increase, decrease, or stay the same? Explain, (c) Find the time referred to in part (b).

Problem 129IP Referring to Example 21-7 Suppose R1 = R2 = 225 ? and R3 = R. The emf of the battery is 12.0 V. (The resistor numbers are given in the Interactive Figure.) (a) Find the value of R such that the current supplied by the battery is 0.0750 A. (b) Find the value of R that gives a potential difference of 2.65 V across resistor 2.

Problem 128IP Referring to Example 21-7 Suppose the three resistors in this circuit have the values R1 = 100.0 ?, R2 = 200.0 ?, and R3 = 300.0 ?, and that the emf of the battery is 12.0 V. (The resistor numbers are given in the Interactive Figure.) (a) Find the potential difference across each resistor, (b) Find the current that flows through each resistor.

Problem 90GP CE Predict/Explain An electric space heater has a power rating of 500 W when connected to a given voltage V. (a) If two of these heaters are connected in series to the same voltage, is the power consumed by the two heaters greater than, less than, or equal to 1000 W? (b) Choose the best explanation from among the following: I. Each heater consumes 500 W; therefore two of them will consume 500 W + 500 W = 1000 W. II. The voltage is the same, but the resistance is doubled by connecting the heaters in scries. Therefore, the power consumed (P = V2/R) is less than 1000 W. III. Connecting two heaters in series doubles the resistance. Since power depends on the resistance squared, it follows that the power consumed is greater than 1000 W.

Problem 91GP CE Two resistors, R1 = R and R2 = 2R, are connected to a battery. (a) Which resistor dissipates more power when they are connected to the battery in series? Explain, (b) Which resistor dissipates more power when they aie connected in parallel? Explain.

Consider the circuit shown in Figure 21–45, in which three lights, each with a resistance R, are connected in series. The circuit also contains an open switch. (a) When the switch is closed, does the intensity of light 2 increase, decrease, or stay the same? Explain. (b) Do the intensities of lights 1 and 3 increase, decrease, or stay the same when the switch is closed? Explain.

The circuit shown in Figure 21–47 shows a resistor and two capacitors connected in series with a battery of voltage V. The circuit also has an ammeter and a switch. Initially, the switch is open and both capacitors are uncharged. The following questions refer to a time long after the switch is closed and current has ceased to flow. (a) In terms of V, what is the voltage across the capacitor \(C_{1}\)? (b) In terms of CV, what is the charge on the right plate of \(C_{2}\)? (c) What is the net charge that flowed through the ammeter during charging? Give your answer in terms of CV. Equation Transcription: Text Transcription: C1 C2 C1=C C2=2C

Problem 101GP Suppose your car carries a charge of 85 ?C. What current does it produce as it travels from Dallas to Fort Worth (35 mi) in 0.75 h?

Problem 104GP It is desired to construct a 5.0-? resistor from a 1.2-m length of tungsten wire. What diameter is needed for this wire?

The three circuits shown in Figure 21–48 have identical batteries, resistors, and capacitors. Initially, the switches are open and the capacitors are uncharged. Rank the circuits in order of increasing (a) final charge on the capacitor and (b) time for the current to drop to \(90 \%\) of its initial value. Indicate ties where appropriate. Equation Transcription: Text Transcription: 90%

Problem 14P The tungsten filament of a lightbulb has a resistance of 0.07 ?. If the filament is 27 cm long, what is its diameter?

Problem 88GP CE Predict/Explain The resistivity of tungsten increases with temperature, (a) When a light containing a tungsten filament heats up, does its power consumption increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The voltage is unchanged, and therefore an increase in resistance implies a reduced power, as we can see from P = V2/R. II. Increasing the resistance increases the power, as is clear from P = I2R. III. The power consumption is independent of resistance, as we can see from P = IV.

Problem 105GP Electrical Safety Codes For safety reasons, electrical codes have been established that limit the amount of current a wire of a given size can carry. For example, an 18-gauge (cross- sectional area = 1.17 mm2), rubber-insulated extension cord with copper wires can carry a maximum current of 5.0 A. Find the voltage drop in a 12-ft, 18-gauge extension cord carrying a current of 5.0 A. (Note: In an extension cord, the current must flow through two lengths—down and back.)

A three-way lightbulb has two filaments with resistances \(R_{1} \text { and } R_{2}\) connected in series. The resistors are connected to three terminals, as indicated in Figure 21–49, and the light switch determines which two of the three terminals are connected to a potential difference of 120 V at any given time. When terminals A and B are connected to 120 V the bulb uses 75.0 W of power. When terminals A and C are connected to 120 V the bulb uses 50.0 W of power. (a) What is the resistance \(R_{1}\)? (b) What is the resistance \(R_{2}\)? (c) How much power does the bulb use when 120 V is connected to terminals B and C? Equation Transcription: Text Transcription: R_1 and R_2 R_1 R_2

Problem 107GP A portable CD player uses a current of 7.5 mA at a potential difference of 3.5 V. (a) How much energy does the player use in 35 s? (b) Suppose the player has a mass of 0.65 kg. For what length of time could the player operate on the energy required to lift it through a height of 1.0 m?

Problem 110GP A silver wire and a copper wire have the same volume and the same resistance. Find the ratio of their radii, r silver/r copper·

Problem 111GP Two resistors are connected in series to a battery with an emf of 12 V. The voltage across the first resistor is 2.7 V and the current through the second resistor is 0.15 A. Find the resistance of the two resistors.