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# College Physics 2017

## Educators

EL
MH ### Problem 1

A battery having an emf of 9.00 $V$ delivers 117 $\mathrm{mA}$ when connected to a $72.0-\Omega$ load. Determine the internal resistance of the battery.

EL
Erica L.
Numerade Educator

### Problem 2

(a) Find the current in an $8.00-\Omega$ resistor connected to a battery that has an internal resistance of 0.15$\Omega$ if the voltage across the battery (the terminal voltage) is 9.00 $\mathrm{V}$ . (b) What is the emf of the battery?

MH
Manish H.
Numerade Educator

### Problem 3

A battery with an emf of 12.0 $\mathrm{V}$ has a terminal voltage of 11.5 $\mathrm{V}$ when the current is 3.00 $\mathrm{A}$ . (a) Calculate the battery's internal resistance $r .$(b) Find the load resistance $R$ . Shoukat A.
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### Problem 4

A battery with a $0.100-\Omega$ internal resistance supplies 15.0 $\mathrm{W}$ of total power with a 9.00 $\mathrm{V}$ terminal voltage. Determine (a) the current $I$ and (b) the power delivered to the load resistor.

MH
Manish H.
Numerade Educator

### Problem 5

Two resistors, $R_{1}$ and $R_{2},$ are connected in series. (a) If $R_{1}=$ 2.00$\Omega$ and $R_{2}=4.00 \Omega$ , calculate the single resistance equivalent to the series combination. (b) Repeat the calculation for a parallel combination of $R_{1}$ and $R_{2} .$ Shoukat A.
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### Problem 6

Three $9.0-\Omega$ resistors are connected in series with a $12-\mathrm{V}$ battery. Find (a) the equivalent resistance of the circuit and (b) the current in each resistor. (c) Repeat for the case in which all three resistors are connected in parallel across the battery.

MH
Manish H.
Numerade Educator

### Problem 7

(a) Find the equivalent resistance between points $a$ and $b$ in Figure P 18.7.
(b) Calculate the current in each resistor if a potential difference of 34.0 V is applied between points $a$ and $b.$ Shoukat A.
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### Problem 8

Consider the combination of resistors shown in Figure $P 18.8$ .
(a) Find the equivalent resistance between point $a$ and $b$ . (b) If a voltage of 35.0 $\mathrm{V}$ is applied between points $a$ and $b$ , find the current in each resistor.

MH
Manish H.
Numerade Educator

### Problem 9

Two resistors connected in series have an equivalent resistance of 690 $\Omega .$ When they are connected in parallel, their equivalent resistance is 150 $\Omega.$ Find the resistance of each resistor. Shoukat A.
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### Problem 10

Consider the circuit shown in Figure P 18.10. (a) Calculate the equivalent resistance of the $10.0-\Omega$ and $5.00-\Omega$ resistors connected in parallel. (b) Using the result of part (a), calculate the combined resistance of the $10.0-\Omega, 5.00-\Omega,$ and $4.00-\Omega$ resistors. (c) Calculate the equivalent resistance of the combined resistance found in part (b) and the parallel $3.00-\Omega$ resistor. (d) Combine the equivalent resistance found in part (c) with the $2.00-\Omega$ resistor. (e) Calculate the total current in the circuit. (f) What is the voltage drop across the $2.00-\Omega$ resistor? (g) Subtracting the result of part (f) from the battery voltage, find the voltage across the $3.00-\Omega$ resistor. (h) Calculate the current in the $3.00-\Omega$ resistor.

MH
Manish H.
Numerade Educator

### Problem 11

Consider the circuit shown in Figure $P 18.11 .$ Find (a) the potential difference between points $a$ and $b$ and (b) the current in the $20.0-\Omega$ resistor. Shoukat A.
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### Problem 12

Four resistors are connected to a battery as shown in Figure P 18.12. (a) Determine the potential difference across each resistor in terms of $\boldsymbol{E} .$ (b) Determine the current in each resistor in terms of $I .$

MH
Manish H.
Numerade Educator

### Problem 13

The resistance between terminals $a$ and $b$ in Figure P 18.13 is 75 $\Omega$ . If the resistors labeled $R$ have the same value, determine $R$ . Shoukat A.
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### Problem 14

A battery with $\boldsymbol{E}=6.00 \mathrm{V}$ and no internal resistance supplies current to the supplies current to the circuit shown in Figure P 18.14. When the double-throw switch $S$ is open as shown in the figure, the current in the battery is 1.00 $\mathrm{mA}$ . When the switch is closed in position $a$ , the current in the battery is 1.20 $\mathrm{mA}$ . When the switch is closed in position $b,$ the current in the battery is 2.00 $\mathrm{mA}$ . Find the resistances (a) $R_{1},$ (b) $R_{2},$ and ( $) R_{3}$ .

MH
Manish H.
Numerade Educator

### Problem 15

Find the current in the $12-\Omega$ resistor in Figure P 18.15. Shoukat A.
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### Problem 16

(a) Is it possible to reduce the circuit shown in Figure P 18.16 to a single equivalent resistor connected across the battery? Explain. (b) Find the current in the $2.00-\Omega$ resistor. (c) Calculate the power delivered by the battery to the circuit.

MH
Manish H.
Numerade Educator

### Problem 17

(a) You need a $45-\Omega$ resistor, but the stockroom has only $20.\Omega$ and $50 . \Omega$ resistors. How can the desired resistance be achieved under these circumstances? (b) What can you do if you need a $35-\Omega$ resistor? Shoukat A.
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### Problem 18

(a) Find the current in each resistor of Figure P 18.18 by using the rules for resistors in series and parallel. (b) Write three independent equations for the three currents using Kirchhoff’s laws: one with the node rule; a second using the loop rule through the battery, the $6.0-\Omega$ resistor, and the $24.0-\Omega$ resistor; and the third using the loop rule through the $12.0-\Omega$ and $24.0-\Omega$ resistors. Solve to check the answers found in part (a).

MH
Manish H.
Numerade Educator

### Problem 19

Figure P 18.19 shows a Wheatstone bridge, a circuit used to precisely measure an unknown resistance R by varying $R_{\mathrm{var}}$ until the ammeter reads zero current and the bridge is said to be "balanced." If the bridge is balanced with $R_{\mathrm{var}}=9.00 \Omega,$ find (a) the value of the unknown resistance $R$ and $(b)$ the current in the $1.00 \Omega$ resistor. (Hint: With the bridge balanced, the wire through the ammeter can effectively be removed from the circuit, leaving two pairs of resistors in parallel.) Shoukat A.
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### Problem 20

For the circuit shown in Figure P 18.20, calculate (a) the current in the $2.00-\Omega$ resistor and (b) the potential difference between points $a$ and $b, \Delta V=V_{b}-V_{a}.$

MH
Manish H.
Numerade Educator

### Problem 21

Taking $R=1.00 \mathrm{k} \Omega$ and $\boldsymbol{E}=250$ $\mathrm{V}$ Figure P 18.21, determine the direction and magnitude of the current in the horizontal wire between $a$ and $e$ Shoukat A.
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### Problem 22

In the circuit of of Figure P 18.22, the current $I_{1}$ is 3.0 $\mathrm{A}$ and the values of $\boldsymbol{E}$ and $R$ are unknown. What are the currents $I_{2}$ and $I_{3} ?$

MH
Manish H.
Numerade Educator

### Problem 23

In the circuit of Figure P 18.23, determine (a) the current in each resistor, (b) the potential difference across the $2.00 \times$ $10^{2}-\Omega$ resistor, and (c) the power delivered by each battery. Shoukat A.
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### Problem 24

Four resistors are connected to a battery with a terminal voltage of 12 $\mathrm{V}$, as shown in Figure P 18.24. (a) How would you reduce the circuit to an equivalent single resistor connected to the battery? Use this procedure to find the equivalent resistance of the circuit. (b) Find the current delivered by the battery to this equivalent resistance. (c) Determine the power delivered by the battery. (d) Determine the power delivered to the $50.0-\Omega$ resistor.

MH
Manish H.
Numerade Educator

### Problem 25

Using Kirchhoff’s rules, (a) find the current in each resistor shown in Figure P 18.25 and (b) find the potential difference between points $c$ and $f.$ Shoukat A.
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### Problem 26

Figure P 18.26 shows a voltage divider, a circuit used to obtain a desired voltage $\Delta V_{\text { out }}$ from a source voltage $\mathcal{E}$ . Determine the required value of $R_{2}$ if $\boldsymbol{E}$ $=5.00 \mathrm{V}, \quad \Delta V_{\mathrm{out}}=1.50 \mathrm{V},$ and $R_{1}=1.00 \times 10^{3} \Omega .$ (Hint: Use Kirchhoff's loop rule, substituting $\Delta V_{\mathrm{out}}=I R_{2},$ to find the
current. Then solve Ohm's law for $R_{2} .)$

MH
Manish H.
Numerade Educator

### Problem 27

(a) Can the circuit shown in Figure P 18.27 be reduced to a single resistor connected to the batteries? Explain. (b) Calculate each of the unknown currents $I_{1}, I_{2},$ and $I_{3}$ for the circuit. Shoukat A.
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### Problem 28

A dead battery is charged by connecting it to the live battery of another car with jumper cables (Fig. P 18.28). Determine the current in (a) the starter and in (b) the dead battery.

MH
Manish H.
Numerade Educator

### Problem 29

(a) Can the circuit shown in Figure P 18.29 be reduced to a single resistor connected to the batteries? Explain. (b) Find the magnitude of the current and its direction in each resistor. Shoukat A.
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### Problem 30

For the circuit shown in Figure P 18.30, use Kirchhoff’s rules to obtain equations for (a) the upper loop, (b) the lower loop, and (c) the node on the left side. In each case suppress units for clarity and simplify, combining like terms. (d) Solve the node equation for $I_{36} .$ (e) Using the equation found in (d), eliminate $I_{36}$ from the equation found in simultaneously for the two unknowns for $I_{18}$ and $I_{12},$ respectively. (g) Substitute the answers found in part (f) into the node equation found in part (d), solving for $I_{36}$ . (h) What is the significance of the negative answer for $I_{12}$?

MH
Manish H.
Numerade Educator

### Problem 31

Find the potential difference across each resistor in Figure P 18.31. Shoukat A.
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### Problem 32

Show that $\tau=R C$ has units of time.

MH
Manish H.
Numerade Educator

### Problem 33

Consider the series $R C$ circuit shown in Figure 18.17 for which $R=75.0 \mathrm{k} \Omega, C=25.0 \mu \mathrm{F},$ and $\boldsymbol{E}=12.0 \mathrm{V}$ . Find (a) the time constant of the circuit and (b) the charge on the capacitor one time constant after the switch is closed. Shoukat A.
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### Problem 34

An uncharged capacitor and a resistor are connected in series to a source of emf. If $\boldsymbol{E}=9.00 \mathrm{V}, C=20.0 \mu \mathrm{F},$ and $R=1.00 \times$ $10^{2} \Omega,$ find (a) the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor after one time constant.

MH
Manish H.
Numerade Educator

### Problem 35

Consider a series $R C$ circuit as in Figure $P 18.35$ for which $R=1.00 \mathrm{M\Omega}, C=$ $5.00 \mu \mathrm{F},$ and $\mathcal{E}=30.0 \mathrm{V}.$ Find (a) the time constant of the circuit and (b) the maximum charge on the capacitor after the switch is thrown closed. (c) Find the current in the resistor 10.0 s after the switch is closed. Shoukat A.
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### Problem 36

The $R C$ charging circuit in a camera flash unit has a volt- age source of 275 $\mathrm{V}$ and a capacitance of 125$\mu \mathrm{F}$ . (a) Find its resistance R if the capacitor charges to 90.0% of its final value in 15.0 s. (b) Find the average current delivered to the flash bulb if the capacitor discharges 90.0% of its full charge in 1.00 ms.

MH
Manish H.
Numerade Educator

### Problem 37

Figure P 18.37 shows a simplified model of a cardiac defibrillator, a device used to resuscitate patients in ventricular fibrillation. When the switch $\mathrm{S}$ is toggled to the left, the capacitor $C$ charges through the resistor $R$ When the switch is toggled to the right, the capacitor discharges current through the patient's torso, modeled as the resistor $R_{\text { torroo }}$ allowing the heart's normal rhythm to be reestablished. (a) If the capacitor is initially uncharged with $C=8.00 \mu \mathrm{F}$ and $\boldsymbol{E}=1250 \mathrm{V}$ , find the value of $R$ required to charge the capacitor to a voltage of 775 $\mathrm{V}$ in 1.50 $\mathrm{s}$ . (b) If the capacitor is then discharged across the patient's torso with $R_{\text { toorso }}=1250 \Omega$ , calculate the voltage across the capacitor after 5.00 $\mathrm{ms} .$ Shoukat A.
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### Problem 38

The capacitor in Figure $P 18.35$ is uncharged for $t<0 .$ If $\boldsymbol{E}=$ $9.00 \mathrm{V}, R=55.0 \Omega,$ and $C=2.00 \mu \mathrm{F}$ , use Kirchhoff's loop rule to find the current through the resistor at the times: (a) $t=0$ , when the switch is closed, and (b) $t=\tau,$ one time constant after the switch is closed.

MH
Manish H.
Numerade Educator

### Problem 39

What minimum number of $75-\mathrm{W}$ light bulbs must be connected in parallel to a single $120-\mathrm{V}$ household circuit to trip a $30.0-\mathrm{A}$ circuit breaker? Shoukat A.
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### Problem 40

A $1150-\mathrm{W}$ toaster and an $825-\mathrm{W}$ microwave oven are connected in parallel to the same $20.0-\mathrm{A}, 120-\mathrm{V}$ circuit. (a) Find the toaster's resistance $R$. (b) If the microwave fails and is replaced, what maximum power rating can be used without tripping the 20.0 -A circuit breaker?

MH
Manish H.
Numerade Educator

### Problem 41

A heating element in a stove is designed to dissipate $3.00 \times 10^{3} \mathrm{W}$ when connected to $240 . \mathrm{V}$ . (a) Assuming the resistance is constant, calculate the current in the heating element if it is connected to $120 . \mathrm{V}$ . (b) Calculate the power it dissipates at that voltage. Shoukat A.
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### Problem 42

A coffee maker is rated at 1 200 W, a toaster at 1 100 W, and a waffle maker at 1 400 W. The three appliances are connected in parallel to a common 120-V household circuit. (a) What is the current in each appliance when operating independently? (b) What total current is delivered to the appliances when all are operating simultaneously? (c) Is a 15-A circuit breaker sufficient in this situation? Explain.

MH
Manish H.
Numerade Educator

### Problem 43

Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited $=$ nerve speed $\times$ pulse duration $=50.0 \mathrm{m} / \mathrm{s} \times 2.0 \times 10^{-3} \mathrm{s}=0.10$ $\mathrm{m}$ ). In the resting state, the outer surface of the axon wall is charged positively with $\mathrm{K}^{+}$ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in Figure $\mathrm{P} 18.43$ . Model the axon as a parallel-plate capacitor and take $C=\kappa \epsilon_{0} A / d$ and $Q=C \Delta V$ to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness $d=1.0 \times 10^{-8} \mathrm{m},$ axon radius $r=1.0 \times 10^{1} \mu \mathrm{m},$ and cell-wall dielectric constant $\kappa=3.0$ . (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. How many $\mathrm{K}^{+}$ ions are on the outside of the axon assuming an initial potential difference of $7.0 \times 10^{-2} \mathrm{V}$ ? Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge $e$ per squared $\left({\mathrm{Å}}^{2}\right) .$ An atom has a cross section of about $1 {\mathrm{Å}}^{2}$ $(1 Å$ $=10^{-10} \mathrm{m} )$. (b) How much positive charge must flow through the cell membrane to reach the excited state of $+3.0 \times 10^{-2} \mathrm{V}$ from the resting state of $-7.0 \times 10^{-2} \mathrm{V}$ ? How many sodium ions (Na^ $^{+} )$ is this? (c) If it takes 2.0 $\mathrm{ms}$ for the $\mathrm{Na}^{+}$ ions to enter the axon, what is the average current in the axon wall in this process? (d) How much energy does it take to raise the potential of the inner axon wall to $+3.0 \times 10^{-2} \mathrm{V},$ starting from the resting potential of $-7.0 \times 10^{-2} \mathrm{V}$ ? Shoukat A.
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### Problem 44

Consider the model of the axon as a capacitor from Problem 43 and Figure P 18.43. (a) How much energy does it take to restore the inner wall of the axon to $-7.0 \times 10^{-2} \mathrm{V}$ , starting from $+3.0 \times 10^{-2} \mathrm{V}$ ? (b) Find the average current in the axon wall during this process.

MH
Manish H.
Numerade Educator

### Problem 45

Using Figure 18.29 b and the results of Problems 18.43 d and 18.44 a, find the power supplied by the axon per action potential. Shoukat A.
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### Problem 46

How many different resistance values can be constructed from a $2.0-\Omega,$ a $4.0-\Omega,$ and a $6.0-\Omega$ resistor? Show how you would get each resistance value either individually or by combining them.

MH
Manish H.
Numerade Educator

### Problem 47

(a) Calculate the potential difference between points $a$ and $b$ in Figure P 18.47 and (b) identify which point is at the higher potential. Shoukat A.
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### Problem 48

For the circuit shown in Figure P 18.48, the voltmeter reads 6.0 $\mathrm{V}$ and the ammeter reads 3.0 $\mathrm{mA}$ . Find (a) the value of $R,$ (b) the emf of the battery, and (c) the voltage across the 3.0 $\mathrm{k} \Omega$ resistor. (d) What assumptions did you have to make to solve this problem?

MH
Manish H.
Numerade Educator

### Problem 49

Figure P 18.49 shows separate series and parallel circuits. (a) What is the ratio $\Delta V_{\text { series }} / \Delta V_{\text { parallel }} ?$ (b) What is the ratio of the power dissipated by the resistors in the series to the parallel circuit, $P_{\text { series }} / P_{\text { parallel }} ?$ Shoukat A.
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### Problem 50

Three 60.0-W, 120-V light- bulbs are connected across a 120-V power source, as shown in Figure P 18.50. Find (a) the total power delivered to the three bulbs and (b) the potential difference across each. Assume the resistance of each bulb is constant (even though, in reality, the resistance increases markedly with current).

MH
Manish H.
Numerade Educator

### Problem 51

When two unknown resistors are connected in series with a battery, the battery delivers 225 W and carries a total current of 5.00 A. For the same total current, 50.0 W is delivered when the resistors are connected in parallel. Determine the value of each resistor. Shoukat A.
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### Problem 52

The circuit in Figure P 18.52 a consists of three resistors and one battery with no internal resistance. (a) Find the current in the $5.00-\Omega$ resistor. (b) Find the power delivered to the $5.00-\Omega$ resistor. (c) In each of the circuits in Figures $\mathrm{P} 18.52 \mathrm{b}$ $\mathrm{P} 18.52 \mathrm{c},$ and $\mathrm{P} 18.52 \mathrm{d},$ an additional $15.0-\mathrm{V}$ battery has been inserted into the circuit. Which diagram or diagrams represent a circuit that requires the use of Kirchhoff’s rules to find the currents? Explain why. (d) In which of these three new circuits is the smallest amount of power delivered to the $10.0-\Omega$ resistor? (You need not calculate the power in each circuit if you explain your answer.)

MH
Manish H.
Numerade Educator

### Problem 53

A circuit consists of three identical lamps, each of resistance $R,$ connected to a battery as in Figure P 18.53. (a) Calculate an expression for the equivalent resistance of the circuit when the switch is open. Repeat the calculation when the switch is closed. (b) Write an expression for the power supplied by the battery when the switch is open. Repeat the calculation when the switch is closed. (c) Using the results already obtained, explain what happens to the brightness of the lamps when the switch is closed. Shoukat A.
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### Problem 54

The resistance between points $a$ and $b$ in Figure $P 18.54$ drops to one-half its original value when switch $S$ is closed. Determine the value of $R .$

MH
Manish H.
Numerade Educator

### Problem 55

The circuit in Figure $P 18.55$ has been connected for several seconds. Find the current (a) in the $4.00-\mathrm{V}$ battery, (b) in the $3.00-\Omega$ resistor, (c) in the $8.00-\mathrm{V}$ battery, and (d) in the $3.00-\mathrm{V}$ battery. (e) Find the charge on the capacitor. Shoukat A.
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### Problem 56

An emf of 10 $\mathrm{V}$ is connected to a series $R C$ circuit consisting of a resistor of $2.0 \times 10^{6} \Omega$ and an initially uncharged capacitor of 3.0$\mu \mathrm{F}$ . Find the time required for the charge on the capacitor to reach 90$\%$ of its final value.

MH
Manish H.
Numerade Educator

### Problem 57

The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (Fig. P 18.57). The unknown resistance $R_{x}$ is between points $C$ and $E$ . Point $E$ is a "true ground" but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earth’s surface. Two identical rods are driven into the ground at $A$ and $B$ , introducing an unknown resistance $R_{r}$ The procedure for finding the unknown resistance $R_{x}$ is as follows. Measure resistance $R_{1}$ between points $A$ and $B$ . Then connect $A$ and $B$ with a heavy conducting wire and measure resistance $R_{2}$ between points $A$ and $C$ . (a) Derive a formula for $R_{x}$ in terms of the observable resistances $R_{1}$ and $R_{2} .$ (b) A satisfactory ground resistance would be $R_{x}<2.0 \Omega .$ Is the grounding of the station adequate if measurements give $R_{1}=13 \Omega$ and $R_{2}=6.0 \Omega ?$ Shoukat A.
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### Problem 58

The resistor $R$ in Figure P 18.58 dissipates 20 W of power. Determine the value of $R.$

MH
Manish H.
Numerade Educator

### Problem 59

A voltage $\Delta V$ is applied to a series configuration of $n$ resistors, each of resistance $R$ . The circuit components are reconnected in a parallel configuration, and voltage $\Delta V$ is again applied. Show that the power consumed by the series configuration is 1$/ n^{2}$ times the power consumed by the parallel configuration. Shoukat A.
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### Problem 60

For the network in Figure Figure P 18.60, show that the resistance between points $a$ and $b$ is $R_{a b}=\frac{27}{17} \Omega .$ (Hint: Connect a battery with emf $\boldsymbol{E}$ across points $a$ and $b$ and determine $\boldsymbol{E} / I,$ where $I$ is the current in the battery.)

MH
Manish H.
Numerade Educator

### Problem 61

A battery with an internal resistance of $10.0 \Omega$ produces an open circuit voltage of 12.0 $\mathrm{V}$ . A variable load resistance with a range from 0 to $30.0 \Omega$ is connected across the battery. (Note: A battery has a resistance that depends on the condition of its chemicals and that increases as the battery ages. This internal resistance can be represented in a simple circuit diagram as a resistor in series with the battery.) (a) Graph the power dissipated in the load resistor as a function of the load resistance. (b) With your graph, demonstrate the following important theorem: The power delivered to a load is a maximum if the load resistance equals the internal resistance of the source. Shoukat A.
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### Problem 62

The circuit in Figure $P 18.62$ contains two resistors, $R_{1}=2.0$ $\mathrm{k} \Omega$ and $R_{2}=3.0 \mathrm{k} \Omega,$ and two capacitors, $C_{1}=2.0 \mu \mathrm{F}$ and $C_{2}=$
$3.0 \mu \mathrm{F},$ connected to a battery with emf $\mathcal{E}=120 \mathrm{V}$ . If there are no charges on the capacitors before switch $\mathrm{S}$ is closed, determine the charges $q_{1}$ and $q_{2}$ on capacitors $C_{1}$ and $C_{2},$ respectively, as functions of time, after the switch is closed. Hint: First reconstruct the circuit so that it becomes a simple $R C$ circuit containing a single resistor and single capacitor in series, connected to the battery, and then determine the total charge $q$ stored in the circuit.

MH
Manish H.
Numerade Educator

### Problem 63

An electric eel generates electric currents through its highly specialized Hunter’s organ, in which thousands of disk-shaped cells called electrocytes are lined up in series, very much in the same way batteries are lined up inside a flashlight. When activated, each electrocyte can maintain a potential difference of about 150 $\mathrm{mV}$ at a current of 1.0 $\mathrm{A}$ for about 2.0 $\mathrm{ms}$ . Suppose a grown electric eel has $4.0 \times 10^{3}$ electrocytes and can
deliver up to $3.00 \times 10^{2}$ shocks in rapid series over about 1.0 $\mathrm{s}$ (a) What maximum electrical power can an electric eel gener- ate? (b) Approximately how much energy does it release in one shock? (c) How high would a mass of 1.0 kg have to be lifted so that its gravitational potential energy equals the energy released in $3.00 \times 10^{2}$ such shocks? Shoukat A.
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### Problem 64

In Figure $\mathrm{P} 18.64, R_{1}=0.100 \Omega$ $R_{2}=1.00 \Omega,$ and $R_{3}=10.0 \Omega.$ Find the equivalent resistance of the circuit and the current in each resistor when a $5.00 \mathrm{V}$ power supply is connected between (a) points $A$ and $B,$ (b) points $A$ and $C,$ and $(\mathrm{c})$ points $A$ and $D.$

MH
Manish H.
Numerade Educator

### Problem 65

What are the expected readings of the ammeter and volt- meter for the circuit in Figure P 18.65? Shoukat A.
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### Problem 66

Consider the two arrangements of batteries and bulbs shown in Figure P 18.66. The two bulbs are identical and have resistance $R,$ and the two batteries are identical with output voltage $\Delta V .$(a) In case $1,$ with the two bulbs in series, compare the brightness of each bulb, the current in each bulb, and the power delivered to each bulb. (b) In case 2, with the two bulbs in parallel, compare the brightness of each bulb, the current in each bulb, and the power supplied to each bulb. (c) Which bulbs are brighter, those in case 1 or those in case 2? (d) In each case, if one bulb fails, will the other go out as well? If the other bulb doesn’t fail, will it get brighter or stay the same? (Problem 66 is courtesy of $E.$ $F.$ Redish. For other problems of this type, visit http://www.physics.umd.edu/perg/.)

MH
Manish H.
Numerade Educator

### Problem 67

The given pair of capacitors in Figure P 18.67 is fully charged by a 12.0-V battery. The battery is disconnected and the circuit closed. After 1.00 ms, how much charge remains on (a) the $3.00-\mu \mathrm{F}$ capacitor? (b) The $2.00-\mu \mathrm{F}$ capacitor? (c) What is the current in the resistor? Shoukat A.
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### Problem 68

A 2.00 -nF capacitor with an initial charge of 5.10$\mu \mathrm{C}$ is discharged through a $1.30-\mathrm{k} \Omega$ resistor. (a) Calculate the magnitude of the current in the resistor 9.00$\mu s$ after the resistor is connected across the terminals of the capacitor. (b) What charge remains on the capacitor after 8.00$\mu \mathrm{s} ?(\mathrm{c})$ What is the maximum current in the resistor?

MH
Manish H.
Numerade Educator