# Physics

## Educators

DS

Problem 1

A flashlight bulb carries a current of 0.38 A for 98 s. How much charge flows through the bulb in this time? How many electrons?

Yaqub K.

Problem 2

Predict/Calculate A car battery does 360 J of work on the charge passing through it as it starts an engine. (a) If the emf of the battery is $12 \mathrm{V},$ how much charge passes through the battery during the start? (b) If the emf is doubled to 24 $\mathrm{V}$ while the work remaing
the same, does the amount of charge passing through the battery
increase or decrease? By what factor?

Yaqub K.

Problem 3

Highly sensitive ammeters can measure currents as small as 10.0 fA. How many electrons per second flow through a wire with a $10.0 .-\mathrm{fA}$ current?

Yaqub K.

Problem 4

A television set connected to a $120-\mathrm{V}$ outlet consumes 21 $\mathrm{w}$ of power. (a) How much current flows through the television? (b) How much time does it take for 10 million electrons to pass through the TV?

Yaqub K.

Problem 5

BiO Pacemaker Batteries Pacemakers designed for long-term use commonly employ a lithium-iodine battery capable of supplying 0.42 $\mathrm{A} \cdot \mathrm{h}$ of charge. (a) How many coulombs of charge can such a battery supply? (b) If the average current produced by the pacemaker is $5.6 \mu \mathrm{A},$ what is the expected lifetime of the device?

Yaqub K.

Problem 6

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

Yaqub K.

Problem 7

CE FlGURE $21-37$ shows a plot of current versus voltage for two different materials, A and
B. Which of these materials satisfies Ohm's law? Explain.

Yaqub K.

Problem 8

CEPredict/Explain Current-versus-voltage plots for two materials, $A$ and $B$ , are shown
in Figure $21-37$ . (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:
I. Curve B is higher in value than curve A.
II. A larger slope means a larger value of $I / V$ , and hence a smaller value of $R .$
III. Curve $B$ has the larger slope at the voltage $V_{1}$ and hence the
larger resistance.

Yaqub K.

Problem 9

A silver wire is 6.9 $\mathrm{m}$ long and 0.79 $\mathrm{mm}$ in diameter. What is its resistance?

Yaqub K.

Problem 10

When a potential difference of 12 $\mathrm{V}$ is applied to a given wire, it conducts 0.45 A of current. What is the resistance of the wire?

Yaqub K.

Problem 11

The tungsten filament of a lightbulb has a resistance of 0.07$\Omega .$ If the filament is 27 $\mathrm{cm}$ long, what is its diameter?

Yaqub K.

Problem 12

A wire is made out of aluminum with a cross-sectional area of $5.25 \times 10^{-4} \mathrm{m}^{2}$ and a length of 65 $\mathrm{km}$ . What is its resistance?

Yaqub K.

Problem 13

Transcranial Direct: Current Stimulation In a tDCS treatment procedure, 0.85 mA of current flows through a patient's brain when there is a $7.4-\mathrm{V}$ potential difference between the electrodes. What
is the equivalent resistance between the electrodes?

Yaqub K.

Problem 14

CE The four conducting cylinders shown in FlGURE $21-38$ 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, $V_{1}, V_{2}, V_{3},$ and $V_{4},$ in order of increasing value. Indicate ties where appropriate.

Yaqub K.

Problem 15

Predict/Calculate A bird lands on a bare copper wire carrying a current of 32 A. The wire is 6 gauge, which means that its cross-sectional area is 0.13 $\mathrm{cm}^{2} .$ (a) Find the difference in potential between the bird's feet, assuming they are separated by a distance of 6.0 $\mathrm{cm}$ . (b) Will your answer to part (a) increase or decrease if the separation between the bird's feet increases? Explain.

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Problem 16

"A current of 0.86 A flows through a copper wire 0.74 $\mathrm{mm}$ in diameter when it is connected to a potential difference of 15 $\mathrm{V}$ . How long is the wire?

Yaqub K.

Problem 17

Predict/Calculate B1O Current Through a Cell Membrane A typical cell membrane is 8.0 $\mathrm{nm}$ thick and has an electrical resistivity of $1.3 \times 10^{7} \Omega \cdot \mathrm{m}$ . (a) If the potential difference between the inner and outer surfaces of a cell membrane is 75 $\mathrm{mV}$ , how much current flows through a square area of membrane 1.0$\mu \mathrm{m}$ 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?

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Problem 18

When a potential difference of 12 $\mathrm{V}$ is applied to a wire 6.9 $\mathrm{m}$ long and 0.33 $\mathrm{mm}$ in diameter, the result is an electric current of 2.1 $\mathrm{A} .$ What is the resistivity of the wire?

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Problem 19

Predict/Calculate (a) What is the resistance per meter of a gold wire with a cross-sectional area of $1.6 \times 10^{-7} \mathrm{m}^{27}$ (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 $2.2 \times 10^{-7} \mathrm{m}^{2}$ .

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Problem 20

BIO Resistance and Current in the Human Finger The interior of the human body has an electrical resistivity of 0.15 $\mathrm{n} \cdot \mathrm{m}$ (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 $\mathrm{mA}$ . What voltage is required to produce this current through your finger?

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Problem 21

Consider a rectangular block of metal of height $A,$ width $B$ and length $C,$ as shown in FIGURE $21-39 .$ If a potential difference $V$ is maintained between the two $A \times B$ 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 $B \times C$ faces of the block. Give your answer in terms of $I_{A B}$ .

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Problem 22

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?

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Problem 23

CE Two lightbulbs 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?

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Problem 24

CE Two lightbulbs 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?

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Problem 25

A $65-\mathrm{V}$ generator supplies 4.8 $\mathrm{kW}$ of power. How much current does the generator produce?

Yaqub K.

Problem 26

A portable CD player operates with a current of 18 $\mathrm{mA}$ at a potential difference of 4.3 $\mathrm{V}$ . What is the power usage of the player?

Yaqub K.

Problem 27

Find the power dissipated in a $22-\Omega$ electric heater connected to a 120 -V outlet.

Yaqub K.

Problem 28

The current in a $120-V$ reading lamp is 2.6 $\mathrm{A}$ . If the cost of electrical energy is $\$ 0.075$per kilowatt-hour, how much does it cost to operate the light for an hour? Check back soon! Problem 29 Circuit$A$in a house has a voltage of 208$\mathrm{V}$and is limited by a 40.0 -A circuit breaker. Circuit$B$is at 120.0$\mathrm{V}$and has a$20.0-\mathrm{A}$circuit breaker. What is the ratio of the maximum power delivered by circuit$\mathrm{A}$to that delivered by circuit$\mathrm{B}$? Check back soon! Problem 30 Predict/Calculate$\mathrm{A} 65$-W lightbulb operates on a potential difference of 95$\mathrm{V}$. 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 65$\mathrm{W}$? By what factor? Check back soon! Problem 31 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$\mathrm{V}$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$\mathrm{V} .$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? Check back soon! Problem 32 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 dissinate less power. Check back soon! Problem 33 CE A circuit consists of three resistors,$R_{1}<R_{2}<R_{3},$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. Check back soon! Problem 34 CEPredict/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. Check back soon! Problem 35$\cdot$What is the minimum number of$88-\Omega$resistors that must be connected in parallel to produce an equivalent resistance of 12$\Omega$or less? Check back soon! Problem 36 Find the equivalent resistance between points A and B for the group of resistors shown in FlGURE$21-40$. Check back soon! Problem 37 A$9.00-\mathrm{V}$battery is connected across the terminals A and$B$for the group of resistors shown in Figure$21-40 .$What is the potential difference across each resistor? Check back soon! Problem 38 Holiday Lights In a string of holiday lights, 50 lights$-$with a resistance of 13.5$\Omega$each$-$are connected in series. (a) If the string of lights is plugged into a$120.0-\mathrm{V}$outlet, what current flows through it? (b) Three of the lights burn out and activate their shunt resistors, effectively reducing the resistance of each one to 0.15$\Omega$. How much current now flows through the entire string of lights? Check back soon! Problem 39 Your toaster has a power cord with a resistance of 0.020$\Omega$connected in series with a$9.6-\Omega$nichrome heating element. If the potential difference between the terminals of the toaster is$120 \mathrm{V},$how much power is dissipated in (a) the power cord and (b) the heating element? Check back soon! Problem 40 A circuit consists of a$12.0-\mathrm{V}$battery connected to three resistors$(37 \Omega, 22 \Omega,$and 141$\mathrm{\Omega})$in series. Find (a) the current that flows through the battery and (b) the potential difference across each resistor. Check back soon! Problem 41 Predict/Calculate Three resistors,$11 \Omega, 53 \Omega,$and$R,$are connected in series with a$24.0-\mathrm{V}$battery. The total current flowing through the battery is 0.16$\mathrm{A}$. (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$\mathrm{V}$, would your answer to part (a) have been larger or smaller? Explain. Check back soon! Problem 42 A circuit consists of a battery connected to three resistors$(65 \Omega, 25 \Omega,$and 170$\Omega)$in parallel. The total current through the resistorsis 2.8$\mathrm{A}$. Find (a) the emf of the battery and (b) the current through each resistor. Check back soon! Problem 43 Predict/Calculate Three resistors,$22 \Omega, 67 \Omega,$and$R,$are connected in parallel with a$12.0-\mathrm{V}$battery. The total current flowing\ through the battery is 0.88$\mathrm{A}$. (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$\mathrm{A}$, would your answer to part (a) have been larger or smaller? Explain. Check back soon! Problem 44 {A} 99-\Omega$ resistor has a current of 0.82 A and is connected in series with a $110-\Omega$ resistor. What is the emf of the battery to which the resistors are connected?

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Problem 45

The equivalent resistance between points A and B of the resistors shown in FlGURE $21-41$ is 33$\Omega$ . Find the value of resistance $R .$

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Problem 46

Find the equivalent resistance between points $A$ and $B$ shown in FIGURE $21-42$ .

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Problem 47

How many $23-W$ lightbulbs can be connected in parallel across a potential difference of 92 $\mathrm{V}$ before the total current in the circuit exceeds 3.0 $\mathrm{A}$ ?

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Problem 48

The circuit in FIGURE $21-43$ 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?

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Problem 49

Predict/Calculate $A 12-V$ battery is connected to terminals $A$ and B in Figure $21-41 .$ (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.

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Problem 50

Predict/Calculate The terminals $A$ and $B$ in Figure $21-42$ are connected to a $9.0-\mathrm{V}$ 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.

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Problem 51

Predict/calculate Suppose the battery in Figure $21-43$ 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.

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Problem 52

Predict/Calculate The current flowing through the $8.45-\Omega$ resistor in HGURE $21-44$ 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.

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Problem 53

Predict/Calculate Four identical resistors are connected to a battery as shown in FiguRE $21-45 .$ 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 $I_{0}$ .

DS
Danielle S.

Problem 54

Find the magnitude and direction (clockwise or counterclockwise) of the current in FlGURE $21-46$ .

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Problem 55

Predict/Calculate Suppose the polarity of the 11.5-V battery in Figure $21-$ 46 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.

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Problem 56

Predict/Calculate It is given that point A in Figure $21-46$ 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.

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Problem 57

Consider the circuit shown in FlGURE $21-47$ . Find the current through each
resistor using (a) the rules for series and parallel resistors and (b) Kirchhoff's rules.

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Problem 58

Suppose point $A$ is grounded $(V=0)$ in Figure $21-47 .$ Find the potential at points $B$ and $C .$

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Problem 59

Predict/Calculate (a) Find the current in each resistor in FlouRE $21-48 .$ (b) Is the potential at point $\mathrm{A}$ greater than, less than, or equal to the potential at point B? Explain.(c) Determine the potential difference between the points A and B.

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Problem 60

Two batteries and three resistors are connected as shown in FlGURE $21-49 .$ How much current flows through each battery when the switch is (a) closed and (b) open?

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Problem 61

CE Two capacitors, $C_{1}=C$ and $C_{2}=2 C$ , 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.

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Problem 62

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.

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Problem 63

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.

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Problem 64

A $252-\mu$ F capacitor is connected in series with a $126-\mu$ F capacitor. What is the equivalent capacitance of the pair?

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Problem 65

A $36-\mu$ F capacitor is connected in parallel with an $18-\mu$ F capacitor. What is the equivalent capacitance of the pair?

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Problem 66

$\cdot$ Find the equivalent capacitance between points A and B for the group of capacitors shown in FlouRE $21-50$ .

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Problem 67

A $15-V$ battery is connected to three capacitors in series. The capacitors have the following capacitances:
4.5 $\mu \mathrm{F}, 12 \mu \mathrm{F}, \quad$ and $\quad 32 \mu \mathrm{F}$ Find the voltage across the $32-\mu \mathrm{F}$ capacitor.

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Problem 68

CE Three different circuits, each containing a switch and two capacitors, are shown in FlouRE $21-51 .$ 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.

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Problem 69

Terminals $A$ and $B$ in Figure $21-50$ are connected to an $18-V$ battery. Find the energy stored in each capacitor.

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Problem 70

Predict/Calculate You would like to add a second capacitor to a $24-\mu$ F capacitor to obtain an equivalent capacitance of 15$\mu \mathrm{F}$ .
(a) Should you connect the second capacitor in series or in parallel with the $24-\mu$ capacitor?
(b) Find the value of the second capacitance you will need.

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Problem 71

Two capacitors, one 7.5$\mu \mathrm{F}$ and the other $15 \mu \mathrm{F},$ are connected in parallel across a $15-\mathrm{V}$ battery. (a) Find the equivalent capacitance of the two capacitors. (b) Find the charge stored in each capacitor. (c) Find the energy stored in each capacitor.

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Problem 72

The equivalent capacitance of the capacitors shown in FlouRE $21-52$ is 12.4$\mu \mathrm{F}$ . Find the value of capacitance $C .$

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Problem 73

With the switch in position $A,$ the $11.2-\mu \mathrm{F}$ capacitor in FIGURE $21-53$ is fully
charged by the $12.0-\mathrm{V}$ battery, and the $9.50-\mu \mathrm{F}$ 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.

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Problem 74

$\cdot$ The switch on an $R C$ circuit is closed at $t=0 .$ Given that $\varepsilon=6.0 \mathrm{V}, R=92 \Omega,$ and $C=28 \mu \mathrm{FF}$ , how much charge is on the capacitor at time $t=4.0 \mathrm{ms}$ ?

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Problem 75

The capacitor in an $R C$ circuit $(R=120 \Omega, C=45 \mu \mathrm{F})$ is initially uncharged. Find (a) the charge on the capacitor and (b) the current in the circuit one time constant $(\tau=R C)$ after the circuit is connected to a $9.0-$ V battery.

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Problem 76

CE 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.

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Problem 77

Consider an $R C$ circuit with $\varepsilon=12.0 \mathrm{V}, R=195 \mathrm{n},$ and $C=45.7 \mu \mathrm{F} .$ Find (a) the time constant for the circuit, (b) the maximum charge on the capacitor, and (c) the initial current in the circuit.

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Problem 78

The resistor in an $R C$ circuit has a resistance of 125$\Omega .$ (a) What capacitance must be used in this circuit if the time constant is to be 4.5 ms? (b) Using the capacitance determined in part (a), calculate the current in the circuit 9.0 ms after the switch is closed. Assume that the capacitor is uncharged initially and that the emf of the battery is 9.0 V.

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Problem 79

A flash unit for a camera has a capacitance of 1500$\mu \mathrm{F}$ . What resistance is needed in this $R C$ circuit if the flash is to charge to 90$\%$ of its full charge in 21 $\mathrm{s}$ ?

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Problem 80

Filouke $21-54$ shows a simplified circuit for a photographic flash unit. This circuit consists of a $9.0-\mathrm{V}$ battery, a 50.0 -k\Omega resistor, a $140-\mu \mathrm{F}$ 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 much time does it take to charge the capacitor to 5.0 $\mathrm{V}$ ?

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Problem 81

Nerve Impulse Propagation The speed with which nerve impulses travel is determined in large part by the characteristic time constant $\tau=R C$ of the circuit formed by the resistivity of the axon
and the capacitance of its wall. The resistance of a 1.00 -mm-long segment of an axon is 25.5 $\mathrm{M} \Omega$ . (a) For nerve axons with no protective myelin sheath, the wall capacitance is about $3.14 \times 10^{-10} \mathrm{F}$ for each segment of length $L=1.00 \mathrm{mm}$ . Find the speed of the nerve impulses given by $v=L / \tau$ . (b) Many axons are surrounded by a myelin sheath that decreases the wall capacitance to $1.57 \times 10^{-12} \mathrm{F}$ . What is the speed of nerve impulses along such myelinated axons?

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Problem 82

Predict/Calculate Consider the $R C$ circuit shown in HGURE $21-55$ . 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.

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Problem 83

CE Consider the circuit shown in FlGURE $21-56,$ 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.

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Problem 84

CE Predict/Explain (a) Referring to Problem 83 and the circuit in Figure $21-56,$ 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.

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Problem 85

CE Consider the circuit shown in FlouRE $21-57,$ 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.

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Problem 86

CE Predict/Explain (a) When the switch is closed in the circuit
shown in Figure $21-57$ , 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 de-
creases 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.

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Problem 87

Suppose that points $\mathrm{A}$ and $\mathrm{B}$ in Figure $21-41$ are connected to
a 12 $\mathrm{-V}$ battery. Find the power dissipated in each of the resistors assuming that $R=65 \Omega .$

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Problem 88

CE The circuit shown in FIGURE $21-58$ 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 $C V,$ 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 $C V$ .

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Problem 89

CE The three circuits shown in FIGURE $21-59$ 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.

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Problem 90

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 $=0.823 \mathrm{mm}^{2}$ ), rubber-insulated extension cord with copper wires can carry a maximum current of 5.0 $\mathrm{A}$ . Find the voltage drop in a $12-\mathrm{ft}$ , 18 -gauge extension cord carrying a current of 5.0 $\mathrm{A}$ . Note: In an extension cord, the current must flow through two lengths - down and back.)

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Problem 91

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

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Problem 92

An electrical heating coil is immersed in 6.6 $\mathrm{kg}$ of water at $22^{\circ} \mathrm{C}$ The coil, which has a resistance of $250 \Omega,$ warms the water to $32^{\circ} \mathrm{C}$ in 15 min. What is the potential difference at which the coil operates?

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Problem 93

Predict/Calculate Consider the circuit shown in FIGURE $21-60$ . (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.

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Problem 94

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

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Problem 95

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 $\mathrm{V}$ . It is desired that the patient receive 75 pulses per minute. Given that the capacitance of the pacemaker is 110$\mu \mathrm{F}$ and that the
battery has a voltage of $9.0 \mathrm{V},$ what value should the resistance have?

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Problem 96

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.

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Problem 97

Predict/Calculate Suppose we connect a 12.0 -V battery to terminals $A$ and $B$ in Figure $21-40$ . (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.

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Problem 98

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 mil $=10^{-3}$ in. Find the maximum power dissipated per length in (a) an 8-gauge wire and (b) a 10 -gauge wire.

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Problem 99

Solar Panel Power The current-versus-voltage plot for a solar panel is shown in FiGuRE $21-61$ . (a) The short-circuit current, $$I_{\mathrm{sc}}$$ of a solar panel is the current it can generate when a wire connects its output terminals, making the load resistance $$R=0$$ What is $$I_{\mathrm{sc}}$$ for this panel? (b) The open-circuit potential, $V_{\alpha c}$ of a solar for this panel? (b) The open-circuit potential, $V_{\alpha c}$ of a solar (infinite load resistance $R$ ). What is $V_{\text { oc }}$ for this panel? (c) Calculate the power output of the solar panel at points $\mathrm{A}, \mathrm{B}$ ,
$\mathrm{C}, \mathrm{D},$ and $\mathrm{E}$ in Figure $21-61 .$

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Problem 100

Predict/Calculate $A 15.0-V$ battery is connected to terminals A and B in Figure $21-52$ . (a) Given that $C=15.0 \mu \mathrm{F}$ , find the charge on each of the capacitors. (b) Find the total energy stored
in this system. (c) If the $7.22-\mu F$ capacitor is increased in value, will the total energy stored in the circuit increase or decrease? Explain.

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Problem 101

When two resistors, $R_{1}$ and $R_{2},$ are connected in series across a 6.0-V battery, the potential difference across $R_{1}$ is 4.0 $\mathrm{V}$ . When $R_{1}$ and $R_{2}$ are connected in parallel to the same battery, the current through $R_{2}$ is 0.45 A. Find the values of $R_{1}$ and $R_{2}$ .

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Problem 102

The circuit shown in FIGURE $21-62$ 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.

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Problem 103

Notice that the experimental setup in Figure $21-63$ is a dc circuit with two resistors in series- the resistance $R$ and the resistance of the person and footwear, $R_{y-1}$ . It follows that the current in the circuit is $1=\varepsilon /\left(R+R_{p t}\right) .$ We also know that the current is
$I=V / R,$ where $V$ is the reading of the voltmeter. These relationships can be combined to relate the voltage $V$ to the resistance $R_{p q}$ with the result shown in FlGURE $21-64$ . According to ANSI regulations, Type II footwear must give a resistance $R_{\text { of }}$ in the range of $0.1 \times 10^{7} \Omega$ to $100 \times 10^{7} Suppose the voltmeter measures a potential difference of 3.70$\mathrm{V}$across the resistor. What is the current that flows through the person's body?$\begin{array}{ll}{\text { A. } 3.70 \times 10^{-6} \mathrm{A}} & {\text { B. } 5.00 \times 10^{-5} \mathrm{A}} \\ {\text { C. } 0.0740 \mathrm{A}} & {\text { D. } 3.70 \mathrm{A}}\end{array}$Check back soon! Problem 104 Notice that the experimental setup in Figure$21-63$is a dc circuit with two resistors in series- the resistance$R$and the resistance of the person and footwear,$R_{y-1}$. It follows that the current in the circuit is$1=\varepsilon /\left(R+R_{p t}\right) .$We also know that the current is$I=V / R,$where$V$is the reading of the voltmeter. These relationships can be combined to relate the voltage$V$to the resistance$R_{p q}$with the result shown in FlGURE$21-64$. According to ANSI regulations, Type II footwear must give a resistance$R_{\text { of }}$in the range of$0.1 \times 10^{7} \Omega$to$100 \times 10^{7} \Omega$What is the resistance of the person and footwear when the voltmeter reads 3.70$\mathrm{V}$?$\begin{array}{ll}{\text { A. } 1.25 \times 10^{7} \Omega} & {\text { B. } 1.35 \times 10^{7} \Omega} \\ {\text { C. } 4.63 \times 10^{7} \Omega} & {\text { D. } 1.71 \times 10^{8} \Omega}\end{array}$Check back soon! Problem 105 Notice that the experimental setup in Figure$21-63$is a dc circuit with two resistors in series- the resistance$R$and the resistance of the person and footwear,$R_{y-1}$. It follows that the current in the circuit is$1=\varepsilon /\left(R+R_{p t}\right) .$We also know that the current is$I=V / R,$where$V$is the reading of the voltmeter. These relationships can be combined to relate the voltage$V$to the resistance$R_{p q}$with the result shown in FlGURE$21-64$. According to ANSI regulations, Type II footwear must give a resistance$R_{\text { of }}$in the range of$0.1 \times 10^{7} \Omega$to$100 \times 10^{7} \Omega$The resistance of a given person and footwear is$4.00 \times 10^{7} \Omega$What is the reading on the voltmeter when this person is tested?$\begin{array}{llll}{\text { A. } 0.976 \mathrm{V}} & {\text { B. } 1.22 \mathrm{V}} & {\text { C. } 1.25 \mathrm{V}} & {\text { D. } 50.0 \mathrm{V}}\end{array}$Check back soon! Problem 106 The standard specifies that footwear should be tested three times: with the person standing on only the left shoe; with the person standing on only the right shoe; and with the person standing on the pair. Do you expect the resistance of the person standing on the left shoe alone to be larger than, smaller than, or the same as the resistance of the person standing on the pair, when measured under the test conditions? Check back soon! Problem 107 REFERRING TO EXAMPLE$21-13$Suppose the three resistors in this circuit have the values$R_{1}=100.0 \Omega, R_{2}=200.0 \Omega,$and$R_{3}=300.0 \Omega,$and the emf of the battery is 12.0$\mathrm{V}$. 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. Check back soon! Problem 108 REFERRING TO EXAMPLE$21-13$Suppose$R_{1}=R_{2}=225 \Omega$and$R_{3}=R .$The emf of the battery is 12.0$\mathrm{V}$. (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$\mathrm{V}$across resistor$2 .$Check back soon! Problem 109 Predict/Calculate REFERING TO EXAMPLE$21-18$Suppose the resistance of the$126-\Omega$resistor is reduced by a factor of$2 .$The other resistor is 275$\Omega$, the capacitor is$182 \mu \mathrm{F},$and the battery has an emf of 3.00$\mathrm{V}$(a) Does the final 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). Check back soon! Problem 110 Predict/ Calculate REFERRING TO EXAMPLE$21-18$Suppose the capacitance of the$182-\mu \mathrm{F}$capacitor is reduced by a factor of$2 .$The two resistors are 126$\Omega$and$275 \Omega,$and the battery has an emf of 3.00$\mathrm{V}$(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).

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