Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

Chapter 20

Electric Circuits - all with Video Answers

Educators

Chapter Questions

Problem 1

A defibrillator is used during a heart attack to restore the heart to its normal beating pattern (see Section 19.5 ). A defibrillator passes 18 A of current through the torso of a person in $2.0 \mathrm{ms}$. (a) How much charge moves during this time? (b) How many electrons pass through the wires connected to the patient?

Netra Sharma

Netra Sharma

University of Wisconsin - Milwaukee

Problem 2

An especially violent lightning bolt has an average current of $1.26 \times$ $10^{3}$ A lasting 0.138 s. How much charge is delivered to the ground by the lightning bolt?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 3

A battery charger is connected to a dead battery and delivers a current of $6.0 \mathrm{A}$ for 5.0 hours, keeping the voltage across the battery terminals at $12 \mathrm{V}$ in the process. How much energy is delivered to the battery?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 4

A coffee-maker contains a heating element that has a resistance of $14 \Omega$ This heating element is energized by a $120-\mathrm{V}$ outlet. What is the current in the heating element?

Vishal Gupta

Numerade Educator

Problem 5

Suppose that the resistance between the walls of a biological cell is $5.0 \times 10^{9} \Omega .$ (a) What is the current when the potential difference between the walls is $75 \mathrm{mV} ?$ (b) If the current is composed of $\mathrm{Na}^{+}$ ions $(q=+e),$ how many such ions flow in $0.50 \mathrm{s} ?$

Netra Sharma

University of Wisconsin - Milwaukee

Problem 6

A car battery has a rating of 220 ampere - hours $(\mathrm{A} \cdot \mathrm{h}) .$ This rating is one indication of the total charge that the battery can provide to a circuit before failing. (a) What is the total charge (in coulombs) that this battery can provide? (b) Determine the maximum current that the battery can provide for 38 minutes.

Vishal Gupta

Numerade Educator

Problem 7

A resistor is connected across the terminals of a $9.0-\mathrm{V}$ battery, which delivers $1.1 \times 10^{5} \mathrm{J}$ of energy to the resistor in six hours. What is the resistance of the resistor?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 8

The resistance of a bagel toaster is $14 \Omega .$ To prepare a bagel, the toaster is operated for one minute from a $120-\mathrm{V}$ outlet. How much energy is delivered to the toaster?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 9

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 10

The resistance and the magnitude of the current depend on the path that the current takes. The drawing shows three situations in which the current takes different paths through a piece of material. Each of the rectangular pieces is made from a material whose resistivity is $\rho=1.50 \times 10^{-2} \Omega \cdot \mathrm{m},$ and the unit of length in the drawing is $L_{0}=5.00 \mathrm{cm} .$ Each piece of material is connected to a $3.00-\mathrm{V}$ battery. Find (a) the resistance and (b) the current in each case.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 11

Two wires are identical, except that one is aluminum and one is copper. The aluminum wire has a resistance of $0.20 \Omega .$ What is the resistance of the copper wire?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 12

A cylindrical wire has a length of $2.80 \mathrm{m}$ and a radius of $1.03 \mathrm{mm}$. It carries a current of 1.35 A, when a voltage of $0.0320 \mathrm{V}$ is applied across the ends of the wire. From what material in Table 20.1 is the wire made?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 13

A coil of wire has a resistance of $38.0 \Omega$ at $25^{\circ} \mathrm{C}$ and $43.7 \Omega$ at $55^{\circ} \mathrm{C}$. What is the temperature coefficient of resistivity?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 14

A large spool in an electrician's workshop has $75 \mathrm{m}$ of insulationcoated wire coiled around it. When the electrician connects a battery to the ends of the spooled wire, the resulting current is $2.4 \mathrm{A} .$ Some weeks later, after cutting off various lengths of wire for use in repairs, the electrician finds that the spooled wire carries a $3.1-$ A current when the same battery is connected to it. What is the length of wire remaining on the spool?

Vishal Gupta

Numerade Educator

Problem 15

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 16

High-voltage power lines are a familiar sight throughout the country. The aluminum wire used for some of these lines has a cross-sectional area of $4.9 \times 10^{-4} \mathrm{m}^{2} .$ What is the resistance of ten kilometers of this wire?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 17

The temperature coefficient of resistivity for the metal gold is 0.0034 $\left(\mathrm{C}^{\circ}\right)^{-1},$ and for tungsten it is $0.0045\left(\mathrm{C}^{\circ}\right)^{-1} .$ The resistance of a gold wire increases by $7.0 \%$ due to an increase in temperature. For the same increase in temperature, what is the percentage increase in the resistance of a tungsten wire?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 18

A tungsten wire has a radius of $0.075 \mathrm{mm}$ and is heated from 20.0 to $1320^{\circ} \mathrm{C} .$ The temperature coefficient of resistivity is $\alpha=4.5 \times$ $10^{-3}\left(\mathrm{C}^{\circ}\right)^{-1} .$ When $120 \mathrm{V}$ is applied across the ends of the hot wire, a current of $1.5 \mathrm{A}$ is produced. How long is the wire? Neglect any effects due to thermal expansion of the wire.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 19

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 20

Two cylindrical rods, one copper and the other iron, are identical in lengths and cross-sectional areas. They are joined end to end to form one long rod. A $12-V$ battery is connected across the free ends of the copper-iron rod. What is the voltage between the ends of the copper rod?

Vishal Gupta

Numerade Educator

Problem 21

A digital thermometer employs a thermistor as the temperaturesensing element. A thermistor is a kind of semiconductor and has a large negative temperature coefficient of resistivity $\alpha .$ Suppose that $\alpha=-0.060\left(\mathrm{C}^{\circ}\right)^{-1}$ for the thermistor in a digital thermometer used to measure the temperature of a patient. The resistance of the thermistor decreases to $85 \%$ of its value at the normal body temperature of $37.0^{\circ} \mathrm{C} .$ What is the patient's temperature?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 22

An electric blanket is connected to a 120 -V outlet and consumes $140 \mathrm{W}$ of power. What is the resistance of the heater wire in the blanket?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 23

The heating element in an iron has a resistance of $24 \Omega .$ The iron is plugged into a $120-\mathrm{V}$ outlet. What is the power delivered to the iron?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 24

A blow-dryer and a vacuum cleaner each operate with a voltage of $120 \mathrm{V}$. The current rating of the blow-dryer is $11 \mathrm{A}$, and that of the vacuum cleaner is $4.0 \mathrm{A}$. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 15 minutes to the energy used by the vacuum cleaner in onehalf hour.

Vishal Gupta

Numerade Educator

Problem 25

There are approximately 110 million households that use TVs in the United States. Each TV uses, on average, $75 \mathrm{W}$ of power and is turned on for 6.0 hours a day. If electrical energy costs $\$ 0.12$ per $k W h,$ how much money is spent every day in keeping 110 million TVs turned on?

Vishal Gupta

Numerade Educator

Problem 26

An MP3 player operates with a voltage of $3.7 \mathrm{V}$, and is using $0.095 \mathrm{W}$ of power. Find the current being supplied by the player's battery.

Vishal Gupta

Numerade Educator

Problem 27

In doing a load of clothes, a clothes dryer uses 16 A of current at $240 \mathrm{V}$ for $45 \mathrm{min} .$ A personal computer, in contrast, uses $2.7 \mathrm{A}$ of current at 120 V. With the energy used by the clothes dryer, how long (in hours) could you use this computer to "surf" the Internet?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 28

An electric heater used to boil small amounts of water consists of a $15-\Omega$ coil that is immersed directly in the water. It operates from a $120-\mathrm{V}$ socket. How much time is required for this heater to raise the temperature of $0.50 \mathrm{kg}$ of water from $13{ }^{\circ} \mathrm{C}$ to the normal boiling point?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 29

The rear window of a van is coated with a layer of ice at $0^{\circ} \mathrm{C} .$ The density of ice is $917 \mathrm{kg} / \mathrm{m}^{3} .$ The driver of the van turns on the rear-window defroster, which operates at $12 \mathrm{V}$ and $23 \mathrm{A}$. The defroster directly heats an area of $0.52 \mathrm{m}^{2}$ of the rear window. What is the maximum thickness of ice coating this area that the defroster can melt in 3.0 minutes?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 30

A piece of Nichrome wire has a radius of $6.5 \times 10^{-4} \mathrm{m}$. It is used in a laboratory to make a heater that uses $4.00 \times 10^{2} \mathrm{W}$ of power when connected to a voltage source of 120 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 31

Tungsten has a temperature coefficient of resistivity of $0.0045\left(\mathrm{C}^{\circ}\right)^{-1} .$ A tungsten wire is connected to a source of constant voltage via a switch. At the instant the switch is closed, the temperature of the wire is $28^{\circ} \mathrm{C},$ and the initial power delivered to the wire is $P_{0} .$ At what wire temperature will the power that is delivered to the wire be decreased to $\frac{1}{2} P_{0} ?$

Netra Sharma

University of Wisconsin - Milwaukee

Problem 32

According to Equation $20.7,$ an ac voltage $V$ is given as a function of time $t$ by $V=V_{0} \sin 2 \pi f t,$ where $V_{0}$ is the peak voltage and $f$ is the frequency (in hertz). For a frequency of $60.0 \mathrm{Hz}$, what is the smallest value of the time at which the voltage equals one-half of the peak value?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 33

The rms current in a copy machine is $6.50 \mathrm{A}$, and the resistance of the machine is $18.6 \Omega .$ What are (a) the average power and (b) the peak power delivered to the machine?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 34

The rms current in a $47-\Omega$ resistor is 0.50 A. What is the peak value of the voltage across this resistor?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 35

A 550 -W space heater is designed for operation in Germany, where household electrical outlets supply $230 \mathrm{V}$ (rms) service. What is the power output of the heater when plugged into a $120-\mathrm{V}$ (rms) electrical outlet in a house in the United States? Ignore the effects of temperature on the heater's resistance.

Vishal Gupta

Numerade Educator

Problem 36

Review Conceptual Example 7 as an aid in solving this problem. A portable electric heater uses 18 A of current. The manufacturer recommends that an extension cord attached to the heater receive no more than
$2.0 \mathrm{W}$ of power per meter of length. What is the smallest radius of copper wire that can be used in the extension cord? (Note: An extension cord contains two wires.)

Netra Sharma

University of Wisconsin - Milwaukee

Problem 37

The average power used by a stereo speaker is 55 W. Assuming that the speaker can be treated as a 4.0-\Omega resistance, find the peak value of the ac voltage applied to the speaker.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 38

The recovery time of a hot water heater is the time required to heat all the water in the unit to the desired temperature. Suppose that a 52 -gal $\left(1.00 \mathrm{gal}=3.79 \times 10^{-3} \mathrm{m}^{3}\right)$ unit starts with cold water at $11^{\circ} \mathrm{C}$ and delivers hot water at $53{ }^{\circ} \mathrm{C}$. The unit is electric and utilizes a resistance heater $(120 \mathrm{V}$ ac, $3.0 \Omega)$ to heat the water. Assuming that no heat is lost to the environment, determine the recovery time (in hours) of the unit.

Vishal Gupta

Numerade Educator

Problem 39

A light bulb is connected to a 120.0 - V wall socket. The current in the bulb depends on the time $t$ according to the relation $I=(0.707 \mathrm{A})$ $\sin [(314 \mathrm{Hz}) t]$ (a) What is the frequency $f$ of the alternating current? (b) Determine the resistance of the bulb's filament. (c) What is the average power delivered to the light bulb?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 40

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 41

Three resistors, $25,45,$ and $75 \Omega,$ are connected in series, and a $0.51-$ A current passes through them. What are (a) the equivalent resistance and (b) the potential difference across the three resistors?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 42

A $60.0-\mathrm{W}$ lamp is placed in series with a resistor and a $120.0-\mathrm{V}$ source. If the voltage across the lamp is $25 \mathrm{V},$ what is the resistance $R$ of the resistor?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 43

The current in a series circuit is 15.0 A. When an additional $8.00-\Omega$ resistor is inserted in series, the current drops to $12.0 \mathrm{A}$. What is the resistance in the original circuit?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 44

Multiple-Concept Example 9 discusses the physics principles used in this problem. Three resistors, $2.0,4.0,$ and $6.0 \Omega,$ are connected in series across a $24-\mathrm{V}$ battery. Find the power delivered to each resistor

Netra Sharma

University of Wisconsin - Milwaukee

Problem 45

The current in a $47-\Omega$ resistor is 0.12 A. This resistor is in series with a $28-\Omega$ resistor, and the series combination is connected across a battery. What is the battery voltage?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 46

Multiple-Concept Example 9 reviews the concepts that are important to this problem. A light bulb is wired in series with a $144-\Omega$ resistor, and they are connected across a $120.0-\mathrm{V}$ source. The power delivered to the light bulb is 23.4 W. What is the resistance of the light bulb? Note that there are two possible answers.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 47

Three resistors are connected in series across a battery. The value of each resistance and its maximum power rating are as follows: $2.0 \Omega$ and $4.0 \mathrm{W}, 12.0 \Omega$ and $10.0 \mathrm{W},$ and $3.0 \Omega$ and $5.0 \mathrm{W}$ (a) What is the greatest voltage that the battery can have without one of the resistors burning up?
(b) How much power does the battery deliver to the circuit in (a)?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 48

One heater uses 340 W of power when connected by itself to a battery. Another heater uses $240 \mathrm{W}$ of power when connected by itself to the same battery. How much total power do the heaters use when they are both connected in series across the battery?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 49

Two resistances, $R_{1}$ and $R_{2},$ are connected in series across a $12-\mathrm{V}$ battery. The current increases by $0.20 \mathrm{A}$ when $R_{2}$ is removed, leaving $R_{1}$ connected across the battery. However, the current increases by just $0.10 \mathrm{A}$ when $R_{1}$ is removed, leaving $R_{2}$ connected across the battery. Find (a) $R_{1}$ and $(b) R_{2}$.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 50

A coffee-maker (14 $\Omega$ ) and a toaster (19 $\Omega$ ) are connected in parallel to the same $120-\mathrm{V}$ outlet in a kitchen. How much total power is supplied to the two appliances when both are turned on?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 51

For the three-way bulb $(50 \mathrm{W}, 100 \mathrm{W}, 150 \mathrm{W})$ discussed in Conceptual Example $11,$ find the resistance of each of the two filaments. Assume that the wattage ratings are not limited by significant figures, and ignore any heating effects on the resistances.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 52

The drawing shows three different resistors in two different circuits. The battery has a voltage of $V=24.0 \mathrm{V}$, and the resistors have values of $R_{1}=50.0 \Omega, R_{2}=25.0 \Omega,$ and $R_{3}=10.0 \Omega .$ (a) For the circuit on the left, determine the current through and the voltage across each resistor. (b) Repeat part (a) for the circuit on the right.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 53

The drawing shows a circuit that contains a battery, two resistors, and a switch. What is the equivalent resistance of the circuit when the switch is (a) open and (b) closed? What is the total power delivered to the resistors when the switch is (c) open and (d) closed?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 54

A $16-\Omega$ loudspeaker, an $8.0-\Omega$ loudspeaker, and a $4.0-\Omega$ loudspeaker are connected in parallel across the terminals of an amplifier. Determine the equivalent resistance of the three speakers, assuming that they all behave as resistors.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 55

Two resistors, 42.0 and 64.0 \Omega, are connected in parallel. The current through the $64.0-\Omega$ resistor is 3.00 A. (a) Determine the current in the other resistor. (b) What is the total power supplied to the two resistors?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 56

Two identical resistors are connected in parallel across a $25-\mathrm{V}$ battery, which supplies them with a total power of $9.6 \mathrm{W}$. While the battery is still connected, one of the resistors is heated so that its resistance doubles. The resistance of the other resistor remains unchanged. Find (a) the initial resistance of each resistor and (b) the total power delivered to the resistors after one resistor has been heated.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 57

A coffee cup heater and a lamp are connected in parallel to the same $120-\mathrm{V}$ outlet. Together, they use a total of $111 \mathrm{W}$ of power. The resistance of the heater is $4.0 \times 10^{2} \Omega .$ Find the resistance of the lamp.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 58

Two resistors have resistances $R_{1}$ and $R_{2}$. When the resistors are connected in series to a $12.0-\mathrm{V}$ battery, the current from the battery is $2.00 \mathrm{A}$. When the resistors are connected in parallel to the battery, the total current from the battery is 9.00 A. Determine $R_{1}$ and $R_{2}$.

Vishal Gupta

Numerade Educator

Problem 59

A cylindrical aluminum pipe of length 1.50 m has an inner radius of $2.00 \times 10^{-3} \mathrm{m}$ and an outer radius of $3.00 \times 10^{-3} \mathrm{m} .$ The interior of the pipe is completely filled with copper. What is the resistance of this unit? (Hint: Imagine that the pipe is connected between the terminals of a battery and decide whether the aluminum and copper parts of the pipe are in series or in parallel.)

Netra Sharma

University of Wisconsin - Milwaukee

Problem 60

The drawing shows two circuits, and the same battery is used in each. The two resistances $R_{\mathrm{A}}$ in circuit $\mathrm{A}$ are the same, and the two resistances $R_{\mathrm{B}}$ in circuit $\mathrm{B}$ are the same. Knowing that the same total power is delivered in each circuit, find the ratio $R_{\mathrm{B}} / R_{\mathrm{A}}$ for the circuits.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 61

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 62

A $60.0-\Omega$ resistor is connected in parallel with a $120.0-\Omega$ resistor This parallel group is connected in series with a $20.0-\Omega$ resistor. The total combination is connected across a $15.0-\mathrm{V}$ battery. Find (a) the current and (b) the power delivered to the $120.0-\Omega$ resistor.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 63

A $14-\Omega$ coffee maker and a $16-\Omega$ frying pan are connected in series across a $120-\mathrm{V}$ source of voltage. A $23-\Omega$ bread maker is also connected across the $120-\mathrm{V}$ source and is in parallel with the series combination. Find the total current supplied by the source of voltage.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 64

Find the equivalent resistance between points $A$ and $B$ in the drawing.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 65

Determine the equivalent resistance between the points $A$ and $B$ for the group of resistors in the drawing.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 66

The circuit in the drawing contains three identical resistors. Each resistor has a value of $10.0 \Omega .$ Determine the equivalent resistance between the points $a$ and $b, b$ and $c,$ and $a$ and $c$.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 67

Find the equivalent resistance between the points $A$ and $B$ in the drawing.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 68

Each resistor in the three circuits in the drawing has the same resistance $R,$ and the batteries have the same voltage $V .$ The values for $R$ and $V$ are $9.0 \Omega$ and $6.0 \mathrm{V},$ respectively. Determine the total power delivered by the battery in each of the three circuits.

Vishal Gupta

Numerade Educator

Problem 69

Eight different values of resistance can be obtained by connecting together three resistors $(1.00,2.00,$ and $3.00 \Omega)$ in all possible ways. What are the values?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 70

Determine the power supplied to each of the resistors in the drawing.

Narayan Hari

Numerade Educator

Problem 71

The circuit in the drawing contains five identical resistors. The $45-\mathrm{V}$ battery delivers $58 \mathrm{W}$ of power to the circuit. What is the resistance $R$ of each resistor?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 72

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 73

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 74

A $1.40-\Omega$ resistor is connected across a $9.00-\mathrm{V}$ battery. The voltage between the terminals of the battery is observed to be only 8.30 V. Find the internal resistance of the battery.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 75

When a light bulb is connected across the terminals of a battery, the battery delivers $24 \mathrm{W}$ of power to the bulb. A voltage of $11.8 \mathrm{V}$ exists between the terminals of the battery, which has an internal resistance of $0.10 \Omega$ What is the emf of the battery?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 76

A battery has an internal resistance of $0.012 \Omega$ and an emf of $9.00 \mathrm{V}$. What is the maximum current that can be drawn from the battery without the terminal voltage dropping below $8.90 \mathrm{V} ?$

Netra Sharma

University of Wisconsin - Milwaukee

Problem 77

A battery delivering a current of 55.0 A to a circuit has a terminal voltage of $23.4 \mathrm{V}$. The electric power being dissipated by the internal resistance of the battery is $34.0 \mathrm{W}$. Find the emf of the battery.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 78

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 79

Consider the circuit in the drawing. Determine (a) the magnitude of the current in the circuit and (b) the magnitude of the voltage between the points labeled $A$ and $B .$ (c) State which point, $A$ or $B,$ is at the higher potential.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 80

The drawing shows a portion of a larger circuit. Current flows left to right in each resistor. What is the current in the resistor $R ?$

Netra Sharma

University of Wisconsin - Milwaukee

Problem 81

Find the magnitude and the direction of the current in the $2.0-\Omega$ resistor in the drawing.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 82

Using Kirchhoff's loop rule, find the value of the current $I$ in part $c$ of the drawing, where $R=5.0 \Omega .$ (Note: Parts $a$ and $b$ of the drawing are used in the online tutorial help that is provided for this problem in the WileyPLUS homework management program.)

Netra Sharma

University of Wisconsin - Milwaukee

Problem 83

Determine the current (both magnitude and direction) in the 8.0 - and $2.0-\Omega$ resistors in the drawing.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 84

Determine the voltage across the $5.0-\Omega$ resistor in the drawing. Which end of the resistor is at the higher potential?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 85

Find the current in the $4.00-\Omega$ resistor in the drawing. Specify the direction of the current.

Vishal Gupta

Numerade Educator

Problem 86

None of the resistors in the circuit shown in the drawing is connected in series or in parallel with one another. Find (a) the current $I_{5}$ and the resistances (b) $R_{2}$ and (c) $R_{3}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 87

The coil of a galvanometer has a resistance of $20.0 \Omega$, and its meter deflects full scale when a current of $6.20 \mathrm{mA}$ passes through it. To make the galvanometer into a nondigital ammeter, a $24.8-\mathrm{m} \Omega$ shunt resistor is added to it. What is the maximum current that this ammeter can read?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 88

The coil of wire in a galvanometer has a resistance of $R_{\mathrm{C}}=60.0 \Omega$ The galvanometer exhibits a full-scale deflection when the current through it is 0.400 mA. A resistor is connected in series with this combination so as to produce a nondigital voltmeter. The voltmeter is to have a full-scale deflection when it measures a potential difference of $10.0 \mathrm{V}$. What is the resistance of this resistor?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 89

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 90

A galvanometer with a coil resistance of $9.00 \Omega$ is used with a shunt resistor to make a nondigital ammeter that has an equivalent resistance of $0.40 \Omega .$ The current in the shunt resistor is $3.00 \mathrm{mA}$ when the galvanometer reads full scale. Find the full-scale current of the galvanometer.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 91

Two scales on a nondigital voltmeter measure voltages up to 20.0 and $30.0 \mathrm{V},$ respectively. The resistance connected in series with the galvanometer is $1680 \Omega$ for the $20.0-\mathrm{V}$ scale and $2930 \Omega$ for the $30.0-\mathrm{V}$ scale. Determine the coil resistance and the full-scale current of the galvanometer that is used in the voltmeter.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 92

In measuring a voltage, a voltmeter uses some current from the circuit. Consequently, the voltage measured is only an approximation to the voltage present when the voltmeter is not connected. Consider a circuit consisting of two $1550-\Omega$ resistors connected in series across a $60.0-\mathrm{V}$ battery. (a) Find the voltage across one of the resistors. (b) A nondigital voltmeter has a full-scale voltage of $60.0 \mathrm{V}$ and uses a galvanometer with a full-scale deflection of $5.00 \mathrm{mA}$. Determine the voltage that this voltmeter registers when it is connected across the resistor used in part (a).

Netra Sharma

University of Wisconsin - Milwaukee

Problem 93

Two capacitors are connected in parallel across the terminals of a battery. One has a capacitance of $2.0 \mu \mathrm{F}$ and the other a capacitance of $4.0 \mu \mathrm{F} .$ These two capacitors together store $5.4 \times 10^{-5} \mathrm{C}$ of charge. What is the voltage of the battery?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 94

Three parallel plate capacitors are connected in series. These capacitors have identical geometries. However, they are filled with three different materials. The dielectric constants of these materials are $3.30,5.40,$ and $6.70 .$ It is desired to replace this series combination with a single parallel plate capacitor. Assuming that this single capacitor has the same geometry as each of the other three capacitors, determine the dielectric constant of the material with which it is filled.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 95

Three capacitors are connected in series. The equivalent capacitance of this combination is $3.00 \mu \mathrm{F}$. Two of the individual capacitances are $6.00 \mu \mathrm{F}$ and $9.00 \mu \mathrm{F} .$ What is the third capacitance (in $\mu \mathrm{F}) ?$

Netra Sharma

University of Wisconsin - Milwaukee

Problem 96

Two capacitors are connected to a battery. The battery voltage is $V=60.0 \mathrm{V},$ and the capacitances are $C_{1}=2.00 \mu \mathrm{F}$ and $C_{2}=4.00 \mu \mathrm{F}$ Determine the total energy stored by the two capacitors when they are wired (a) in parallel and (b) in series.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 97

Determine the equivalent capacitance between $A$ and $B$ for the group of capacitors in the drawing.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 98

A $2.00-\mu \mathrm{F}$ and a $4.00-\mu \mathrm{F}$ capacitor are connected to a $60.0-\mathrm{V}$ battery. What is the total charge supplied to the capacitors when they are wired (a) in parallel and (b) in series with each other?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 99

Suppose that two capacitors $\left(C_{1}\right.$ and $\left.C_{2}\right)$ are connected in series. Show that the sum of the energies stored in these capacitors is equal to the energy stored in the equivalent capacitor. [Hint: The energy stored in a capacitor can be expressed as $\left.q^{2} /(2 C) .\right]$

Vishal Gupta

Numerade Educator

Problem 100

A $3.00-\mu \mathrm{F}$ and a $5.00-\mu \mathrm{F}$ capacitor are connected in series across a $30.0-\mathrm{V}$ battery. A $7.00-\mu \mathrm{F}$ capacitor is then connected in parallel across the $3.00-\mu \mathrm{F}$ capacitor. Determine the voltage across the $7.00-\mu \mathrm{F}$ capacitor.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 101

A $7.0-\mu \mathrm{F}$ and a $3.0-\mu \mathrm{F}$ capacitor are connected in series across a $24-\mathrm{V}$ battery. What voltage is required to charge a parallel combination of the two capacitors to the same total energy?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 102

The drawing shows two capacitors that are fully charged $\left(C_{1}=\right.$ $\left.2.00 \mu \mathrm{F}, q_{1}=6.00 \mu \mathrm{C} ; C_{2}=8.00 \mu \mathrm{F}, q_{2}=12.0 \mu \mathrm{C}\right) .$ The switch is closed
and charge flows until equilibrium is reestablished (i.e., until both capacitors have the same voltage across their plates). Find the resulting voltage across either capacitor.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 103

In a heart pacemaker, a pulse is delivered to the heart 81 times per minute. The capacitor that controls this pulsing rate discharges through a resistance of $1.8 \times 10^{6} \Omega .$ One pulse is delivered every time the fully charged capacitor loses $63.2 \%$ of its original charge. What is the capacitance of the capacitor?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 104

A circuit contains a resistor in series with a capacitor, the series combination being connected across the terminals of a battery, as in Figure $20.37 a .$ The time constant for charging the capacitor is $1.5 \mathrm{s}$ when the resistor has a resistance of $2.0 \times 10^{4} \Omega .$ What would the time constant be if the resistance had a value of $5.2 \times 10^{4} \Omega ?$

Vishal Gupta

Numerade Educator

Problem 105

The circuit in the drawing contains two resistors and two capacitors that are connected to a battery via a switch. When the switch is closed, the capacitors begin to charge up. What is the time constant for the charging process?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 106

??w many time constants must elapse before a capacitor in a series $R C$ circuit is charged to $80.0 \%$ of its equilibrium charge?

Vishal Gupta

Numerade Educator

Problem 107

Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part $a$ of the drawing, the time constant to charge up this circuit is 0.72 s. What is the time constant when they are connected with the same resistor, as in part $b ?$

Netra Sharma

University of Wisconsin - Milwaukee

Problem 108

Each of the four circuits in the drawing consists of a single resistor whose resistance is either $R$ or $2 R,$ and a single battery whose voltage is either $V$ or $2 V .$ The unit of voltage in each circuit is $V=12.0 \mathrm{V}$ and the unit of resistance is $R=6.00 \Omega .$ Determine (a) the power supplied to each resistor and (b) the current delivered to each resistor.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 109

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 110

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 111

In the Arctic, electric socks are useful. A pair of socks uses a $9.0-\mathrm{V}$ battery pack for each sock. A current of $0.11 \mathrm{A}$ is drawn from each battery pack by wire woven into the socks. Find the resistance of the wire in one sock.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 112

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 113

In Section 12.3 it was mentioned that temperatures are often measured with electrical resistance thermometers made of platinum wire. Suppose that the resistance of a platinum resistance thermometer is $125 \Omega$ when its temperature is $20.0^{\circ} \mathrm{C}$. The wire is then immersed in boiling chlorine, and the resistance drops to $99.6 \Omega$. The temperature coefficient of resistivity of platinum is $\alpha=3.72 \times 10^{-3}\left(\mathrm{C}^{\circ}\right)^{-1} .$ What is the temperature of the boiling chlorine?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 114

The circuit in the drawing shows two resistors, a capacitor, and a battery. When the capacitor is fully charged, what is the magnitude $q$ of the charge on one of its plates?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 115

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 116

An $86-\Omega$ resistor and a $67-\Omega$ resistor are connected in series across a battery. The voltage across the $86-\Omega$ resistor is 27 V. What is the voltage across the $67-\Omega$ resistor?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 117

The current in the $8.00-\Omega$ resistor in the drawing is 0.500 A. Find the current in (a) the $20.0-\Omega$ resistor and in $(b)$ the $9.00-\Omega$ resistor.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 118

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 119

An extension cord is used with an electric weed trimmer that has a resistance of $15.0 \Omega .$ The extension cord is made of copper wire that has a cross-sectional area of $1.3 \times 10^{-6} \mathrm{m}^{2} .$ The combined length of the two wires in the extension cord is $92 \mathrm{m}$. (a) Determine the resistance of the extension cord. (b) The extension cord is plugged into a $120-\mathrm{V}$ socket. What voltage is applied to the trimmer itself?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 120

The total current delivered to a number of devices connected in parallel is the sum of the individual currents in each device. Circuit breakers are resettable automatic switches that protect against a dangerously large total current by "opening" to stop the current at a specified safe value. A $1650-\mathrm{W}$ toaster, a $1090-\mathrm{W}$ iron, and a $1250-\mathrm{W}$ microwave oven are turned on in a kitchen. As the drawing shows, they are all connected through a $20-\mathrm{A}$ circuit breaker (which has negligible resistance) to an ac voltage of $120 \mathrm{V}$
(a) Find the equivalent resistance of the three devices. (b) Obtain the total current delivered by the source and determine whether the breaker will "open" to prevent an accident.

Netra Sharma

University of Wisconsin - Milwaukee

Problem 121

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 122

The filament in an incandescent light bulb is made from tungsten. The light bulb is plugged into a $120-\mathrm{V}$ outlet and draws a current of $1.24 \mathrm{A}$. If the radius of the tungsten wire is $0.0030 \mathrm{mm},$ how long must the wire be?

Netra Sharma

University of Wisconsin - Milwaukee

Problem 123

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 124

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 125

A circuit contains a 48-V battery and a single light bulb whose resistance is $240 \Omega .$ A second, identical, light bulb can be wired either in series or in parallel with the first one (see the figure). Concepts: (i) How is the power $P$ that is delivered to a light bulb related to the bulb's resistance $R$ and the voltage $V$ across it? (ii) When there is only one bulb in the circuit, what is the voltage across it? (iii) The more power delivered to a bulb, the brighter it is. When two bulbs are wired in series, does the brightness of each bulb increase, decrease, or remain the same relative to the brightness of the bulb in the single-bulb circuit? (iv) When two bulbs are wired in parallel, does the brightness of each bulb increase, decrease, or remain the same relative to the brightness of the bulb in the single-bulb circuit? Calculations: Determine the power delivered to a single bulb when the circuit contains (a) only one bulb, (b) two bulbs in series and (c) two bulbs in parallel. Assume that the battery has no internal resistance.

Vishal Gupta

Numerade Educator

Problem 126

For this problem concerning Kirchhoff's junction rule and loop rule, refer to the figure. Concepts: (i) Notice that there are two loops, labeled 1 and 2 in this circuit. Does it matter that there is no battery in loop 1 but only two resistors? Explain. (ii) The currents through the three resistors are labeled as $I_{1}, I_{2},$ and $I_{3} .$ Does it matter which direction, left-to-right or right-to-left, has been chosen for each circuit? (iii) When we place $+$ and $-$ signs on the ends of each resistor, does it matter which side is $+$ and which is $-?$ (iv) When we evaluate the potential drops and rises around a closed loop, does it matter which direction, clockwise or counterclockwise, is chosen for the evaluation? Calculations: Use Kirchhoff's junction and loop rules to determine the currents through the three resistors.

Vishal Gupta

Numerade Educator

Problem 127

You and your team are stranded on a tropical island that hosts a deserted military base. In your efforts to get rescued, you find a radio. However, when you power it up some lights turn on, but the radio does not transmit or receive. You open up the back cover and quickly identify the problem: There is a burnt resistor on the circuit board. You have located some basic electronics tools and supplies, but the charred resistor is unidentifiable, so you do not know what to use for its replacement. There is a crude schematic on the inside of the cover of the radio, but it only gives the value of the current through the part of the circuit with the burnt resistor. You sketch the circuit with all the elements you can identify (see drawing). (a) Determine the value of the damaged resistor. (b) The next problem is that the resistors that you have found are all $47.0 \Omega .$ The available space will only allow for six or fewer resistors. Find a configuration of six or fewer $47.0-\Omega$ resistors that has an equivalent resistance within $10 \%$ of that calculated in part (a).

Vishal Gupta

Numerade Educator

Problem 128

You and your team are designing a small tube heater that consists of a small ceramic tube wrapped with a special heater wire composed of Nichrome. When you run an electrical current through the wire, the wire (and therefore the tube) heats up through resistive heating. Nichrome is an alloy composed of $80 \%$ nickel and $20 \%$ chromium, and has a resistivity of $\rho=1.25 \times 10^{-6} \Omega \cdot \mathrm{m} .$ (a) What is the resistance per centimeter of 28-gauge Nichrome wire? ("28 gauge" means the wire has a diameter $D=0.320 \mathrm{mm}$ (b) You wrap the tube with $45.0 \mathrm{cm}$ of the Nichrome wire, and you want the power output of your heater to be $120 \mathrm{W}$. What current is needed? (c) What voltage will provide the current calculated in (b)?

Vishal Gupta

Numerade Educator