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College Physics

Raymond A. Serway, Jerry S. Faughn, Chris Vuille

Chapter 18

Direct-Current Circuits - all with Video Answers

Educators

DM

Chapter Questions

01:24

Problem 1

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

Manish Kumar ( Iit K )
Manish Kumar ( Iit K )
Numerade Educator
05:30

Problem 2

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.

Manish Haldankar
Manish Haldankar
Numerade Educator
03:27

Problem 3

A lightbulb marked -75W [at] $120 \mathrm{~V}^{\prime \prime}$ is screwed into a socket at one end of a long extension cord in which each of the two conductors has a resistance of $0.800 \Omega$. The other end of the extension cord is plugged into a $120-\mathrm{V}$ outlet. Draw a circuit diagram, and find the actual power of the bulb in the circuit described.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:25

Problem 4

(a) Find the current in a $8.00-\Omega$ 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?

Manish Haldankar
Manish Haldankar
Numerade Educator
03:33

Problem 5

(a) Find the equivalent resistance between points $a$ and $b$ in Figure $P 18.5 .$ (b) Calculate the current in each resistor if a potential difference of $34.0 \mathrm{~V}$ is applied between points $a$ and $b$.

Shoukat Ali
Shoukat Ali
Other Schools
02:10

Problem 6

Consider the combination of resistors shown in Figure P18.6. (a) Find the equivalent resistance between point $a$ and $b$. (b) If a voltage of $35 \mathrm{~V}$ is applied between points $a$ and $b$, find the current in each resistor.

Manish Kumar ( Iit K )
Manish Kumar ( Iit K )
Numerade Educator
01:06

Problem 7

What is the equivalent resistance of the combination of identical resistors between points $a$ and $b$ in Figure $P 18,7 ?$

Manish Kumar ( Iit K )
Manish Kumar ( Iit K )
Numerade Educator
13:04

Problem 8

Consider the circuit shown in Figure P18.8. (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.

Manish Haldankar
Manish Haldankar
Numerade Educator
11:11

Problem 9

Consider the circuit shown in Figure P18.9. Find (a) the current in the $20.0-\Omega$ resistor and $(b)$ the potential difference between points $a$ and $b$.

Chris Johnson
Chris Johnson
Numerade Educator
01:42

Problem 10

Consider the two circuits shown in Figure $\mathrm{P} 18.10 \mathrm{in}$ which the lightbulbs and batteries are identical. The resistance of each lightbulb is $R$. (a) Find the currents in each lightbulb. (b) How does the brightness of B compare with that of C? Explain. (c) How does the brightness of A compare with that of $\mathrm{B}$ and $\mathrm{C}$ ? Explain.

Manish Kumar ( Iit K )
Manish Kumar ( Iit K )
Numerade Educator
03:01

Problem 11

The resistance between terminals $a$ and $b$ in Figure $\mathrm{P} 18.11$ is $75 \Omega$. If the resistors labeled $R$ have the same value, determine $R$

Shoukat Ali
Shoukat Ali
Other Schools
05:19

Problem 12

Three identical resistors are connected as shown in Figure P18.12. The maximum power that can safely be delivered by a battery connected between $a$ and $b$ is $24 \mathrm{~W}$.
(a) What is the equivalent resistance between points $a$ and be (b) Find an expression for the maximum voltage that can be applied between $a$ and $b .$ (c) What is the power delivered to each resistor when the maximum voltage is applied between $a$ and $b ?$

Luis Rios
Luis Rios
Numerade Educator
04:42

Problem 13

Find the current in the $12-\Omega$ resistor in Figure $\mathrm{P} 18.13$.

Shoukat Ali
Shoukat Ali
Other Schools
04:56

Problem 14

Is it possible to reduce the circuit shown in Figure P18.14 (page 620 ) 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.

Luis Rios
Luis Rios
Numerade Educator
03:16

Problem 15

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

Luis Rios
Luis Rios
Numerade Educator
08:48

Problem 16

Find the current in each resistor of Figure $\mathrm{P} 18.16$ by using the rules for resistors in series and parallel.
(b) Write three independent equations for the three currents using Kirchoff'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).

Vishal Gupta
Vishal Gupta
Numerade Educator
06:29

Problem 17

The ammeter shown in Figure $\mathrm{P} 18.17$ reads $2.00 \mathrm{~A}$. Find $I_{1}, I_{2}$, and $\varepsilon_{-}$

Luis Rios
Luis Rios
Numerade Educator
03:59

Problem 18

Determine the potential difference $\Delta V_{a \phi}$ for the circuit in Figure $\mathrm{P} 18.18 .$

Shoukat Ali
Shoukat Ali
Other Schools
07:59

Problem 19

Figure P18.19 shows a circuit diagram. Determine (a) the current, (b) the potential of wire $A$ relative to ground, and (c) the voltage drop across the $1500-\Omega$ resistor.

Vishal Gupta
Vishal Gupta
Numerade Educator
04:01

Problem 20

In the circuit of Figure $\mathrm{P} 18.20$, the current $I_{1}$ is $3.0 \mathrm{~A}$ and the values of $\varepsilon$ and $R$ are unknown. What are the currents $I_{2}$ and $I_{3} ?$

Luis Rios
Luis Rios
Numerade Educator
11:56

Problem 21

(a) In Figure P18.21 find the current in each resistor and
(b) the power delivered to each resistor.

Luis Rios
Luis Rios
Numerade Educator
14:30

Problem 22

Four resistors are connected to a battery with a terminal voltage of $12 \mathrm{~V}$, as shown in Figure $\mathrm{P} 18.22 .$ (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.

Manish Haldankar
Manish Haldankar
Numerade Educator
09:25

Problem 23

Uusing Kirchhoff's rules, (a) find the current in each resistor shown in Figure P18.23 and (b) find the potential difference between points $c$ and $f$.

Vishal Gupta
Vishal Gupta
Numerade Educator
06:05

Problem 24

Two $1.50-\mathrm{V}$ batteries-with their positive terminals in the same direction-are inserted in series into the barrel of a flashlight. One battery has an internal resistance of $0.255 \Omega$, the other an internal resistance of $0.15 . \Omega$. When the switch is closed, a current of $0.600 \mathrm{~A}$ passes through the lamp. (a) What is the lamp's resistance?
(b) What fraction of the power dissipated is dissipated in the batteries?

Vishal Gupta
Vishal Gupta
Numerade Educator
11:19

Problem 25

Can the circuit shown in Figure P18.25 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.

Luis Rios
Luis Rios
Numerade Educator
03:25

Problem 26

A dead battery is charged by connecting it to the live battery of another car with jumper cables (Fig. $\mathrm{P} 18.26)$. Determine the current in the starter and in the dead battery.

Sophie S
Sophie S
Numerade Educator
11:50

Problem 27

Can the circuit shown in Figure P18.27 be reduced to a single resistor connected to the batteries? Explain. (b) Find the magnitude of the current and its direction in each resistor.

Luis Rios
Luis Rios
Numerade Educator
17:43

Problem 28

For the circuit shown in Figure P18.28, 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 part (b). (f) Solve the equations found in part (a) and part (e) 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 $I_{12} ?$

Manish Haldankar
Manish Haldankar
Numerade Educator
03:59

Problem 29

Find the potential difference across each resistor in Figure $\mathrm{P} 18.29$.

Shoukat Ali
Shoukat Ali
Other Schools
05:12

Problem 30

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

Manish Haldankar
Manish Haldankar
Numerade Educator
03:27

Problem 31

Consider the series RC-circuit shown in Active Figure $18.16$ for which $R=75.0 \mathrm{k} \Omega, C=25.0 \mu \mathrm{F}$, and $\varepsilon=$
$12.0 \mathrm{~V}$. Find (a) the time constant of the circuit and (b) the charge on the capacitor one time constant after the switch is closed.

Luis Rios
Luis Rios
Numerade Educator
03:17

Problem 32

An uncharged capacitor and a resistor are connected in series to a source of emf. If $\varepsilon=9.00 \mathrm{~V}, C=20.0 \mu \mathrm{F}$, and $R=100 \Omega$, 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.

Luis Rios
Luis Rios
Numerade Educator
02:17

Problem 33

Consider a series $R C$ circuit for which $R=1.0 \mathrm{M} \Omega, C=$ $5.0 \mu \mathrm{F}$, and $\varepsilon=30 \mathrm{~V}$. Find the charge on the capacitor $10 \mathrm{~s}$ after the switch is closed.

Luis Rios
Luis Rios
Numerade Educator
03:00

Problem 34

A series combination of a $12-\mathrm{k} \Omega$ resistor and an unknown capacitor is connected to a $12-V$ battery. One second after the circuit is completed, the voltage across the capacitor is $10 \mathrm{~V}$. Determine the capacitance of the capacitor.

Luis Rios
Luis Rios
Numerade Educator
03:34

Problem 35

A charged capacitor is connected to a resistor and a switch as in Active Figure $18.17$. The circuit has a time constant of $1.5 \mathrm{~s}$. After the switch is closed, the charge on the capacitor is $75 \%$ of its initial charge. (a) Find the time it takes to reach this charge, (b) If $R=250 \mathrm{k} \Omega$, what is the value of $C$ ?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:08

Problem 36

A series $R C$ circuit has a time constant of $0.960 \mathrm{~s}$. The battery has an emf of $48.0 \mathrm{~V}$, and the maximum current in the circuit is $0.500 \mathrm{~mA}$. What are (a) the value of the capacitance and (b) the charge stored in the capacitor $1.92 \mathrm{~s}$ after the switch is closed?

Luis Rios
Luis Rios
Numerade Educator
04:27

Problem 37

What minimum number of $75-W$ lightbulbs must be connected in parallel to a single $120-\mathrm{V}$ household circuit to trip a $30.0$ -A circuit breaker?

Luis Rios
Luis Rios
Numerade Educator
06:25

Problem 38

A lamp $(R=150 \Omega)$, an electric heater $(R=25 \Omega)$, and a fan $(R=50 \Omega)$ are connected in parallel across a $120-\mathrm{V}$ line. (a) What total current is supplied to the circuit? (b) What is the voltage across the fan? (c) What is the current in the lamp? (d) What power is expended in the heater?

Luis Rios
Luis Rios
Numerade Educator
02:44

Problem 39

A heating element in a stove is designed to dissipate $3000 \mathrm{~W}$ 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.

Luis Rios
Luis Rios
Numerade Educator
05:13

Problem 40

A coffee maker is rated at $1200 \mathrm{~W}$, a toaster at $1100 \mathrm{~W}$, and a waffle maker at $1400 \mathrm{~W}$. The three appliances are connected in parallel to a common $120-\mathrm{V}$ household circuit. (a) What is the current in each appliance when operating independently? (b) What total cuirent is delivered to the appliances when all are operating simultaneously: (c) Is a $15-\mathrm{A}$ circuit breaker sufficient in this situation? Explain.

Luis Rios
Luis Rios
Numerade Educator
07:04

Problem 41

Assume a length of axon membrane of about $0.10 \mathrm{~m}$ 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 P18.41. Model the axon as a parallelplate 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 $0.10-\mathrm{m}$ 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 the number of angstroms $\left(\AA^{2}\right)$ per electronic charge. An atom has a cross section of about $\left.1 \mathrm{~A}^{2}\left(1 \AA \mathrm{A}=10^{-10} \mathrm{~m}\right) .\right]$ (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 $-7.0 \times 10^{-2}$ V? How many sodium ions (Nat) 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 Ali
Shoukat Ali
Other Schools
04:33

Problem 42

Consider the model of the axon as a capacitor from Problem 41 and Figure P18.41. (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 $+3.0 \times 10^{-2} \mathrm{~V}_{\mathrm{f}}$
(b) Find the average current in the axon wall during this process.

Eduard Sanchez
Eduard Sanchez
Numerade Educator
02:15

Problem 43

Using Figure $18.28 \mathrm{~b}$ and the results of Problems $18.41 \mathrm{~d}$ and $18.42 \mathrm{a}$, find the power supplied by the axon per action potential.

Eduard Sanchez
Eduard Sanchez
Numerade Educator
04:17

Problem 44

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.

DM
Debra Mangion
Numerade Educator
03:29

Problem 45

Find the equivalent resistance between points $a$ and $b$ in Figure $\mathrm{P} 18.45$.

Vishal Gupta
Vishal Gupta
Numerade Educator
05:30

Problem 46

For the circuit shown in Figure $\mathrm{P} 18.46$, the voltmeter reads $6.0 \mathrm{~V}$ and the ammeter reads $3.0 \mathrm{~m} \mathrm{~A}$. Find (a) the value of $R,(b)$ the emf of the battery, and (c) the voltage across the $3,0-\mathrm{kV}$ resistor. (d) What assumptions did you have to make to solve this problem?

Vishal Gupta
Vishal Gupta
Numerade Educator
10:38

Problem 47

Find (a) the equivalent resistance of the circuit in Figure $\mathrm{P} 18.47$, (b) each current in the circuit, (c) the potential difference across each resistor, and (d) the power dissipated by cach resistor.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
04:51

Problem 48

Three $60.0-\mathrm{W}, 120-\mathrm{V}$ lightbulbs are connected across a $120-V$ power source, as shown in Figure PI8.48. 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).

Vishal Gupta
Vishal Gupta
Numerade Educator
05:22

Problem 49

An automobile battery has an emf of $12.6 \mathrm{~V}$ and an internal resistance of $0.080 \Omega$. The headlights have a total resistance of $5.00 \Omega$ (assumed constant). What is the potential difference across the headlight bulbs (a) when they are the only load on the battery and (b) when the starter motor is operated, taking an additional $35.0 \mathrm{~A}$ from the battery?

Luis Rios
Luis Rios
Numerade Educator
05:33

Problem 50

In Figure $P 18.50$ suppose the switch has been closed for a length of time sufficiently long for the capacitor to become fully charged. Find (a) the steady-state current in cach resistor and (b) the charge on the capacitor.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:58

Problem 51

A circuit consists of three identical lamps, each of resistance $R$, connected to a battery as in Figure $\mathrm{P} 18.51 .$
(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 Ali
Shoukat Ali
Other Schools
10:19

Problem 52

The resistance between points $a$ and $b$ in Figure $\mathrm{P} 18.52$ drops to one-half its original value when switch $\mathrm{S}$ is closed. Determine the value of $R$.

Manish Haldankar
Manish Haldankar
Numerade Educator
03:01

Problem 53

A generator has a terminal voltage of $110 \mathrm{~V}$ when it delivers $10.0 \mathrm{~A}$ and $106 \mathrm{~V}$ when it delivers $30.0 \mathrm{~A}$. Calculate the emfand the internal resistance of the generator.

Luis Rios
Luis Rios
Numerade Educator
04:08

Problem 54

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

Luis Rios
Luis Rios
Numerade Educator
02:17

Problem 55

The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (Fig. P18.55, page 624). 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 suratum 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 $R_{\text {r. }}$ 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 Ali
Shoukat Ali
Other Schools
15:38

Problem 56

The resistor $R$ in Figure $\mathrm{P} 18.56$ dissipates $20 \mathrm{~W}$ of power. Determine the value of $R$.

Manish Haldankar
Manish Haldankar
Numerade Educator
01:37

Problem 57

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 Ali
Shoukat Ali
Other Schools
07:40

Problem 58

For the network in Figure $\mathrm{P} 18.58$, show that the resistance between points $a$ and $b$ is $R_{a b}=\frac{27}{17} \Omega$. (Hint: Connect a battery with emf $\varepsilon$ across points $a$ and $b$ and determine $\varepsilon / I$. where $I$ is the current in the battery.)

Manish Haldankar
Manish Haldankar
Numerade Educator
01:35

Problem 59

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. (Nole. A battery has a resistance that depends on the condition of its chemicals and that increases as the bauery 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 Ali
Shoukat Ali
Other Schools
06:52

Problem 60

The circuit in Figure $\mathrm{P} 18.60$ 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 $\operatorname{emf} \varepsilon=$ $120 \mathrm{~V}$. If there are no charges on the capacitors before switch $S$ 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.)

Eduard Sanchez
Eduard Sanchez
Numerade Educator
03:03

Problem 61

Consider the circuit shown in Figure P18.61. Find (a) the potential difference between points $a$ and $b$ and (b) the current in the $20.0-\Omega$ resistor.

Shoukat Ali
Shoukat Ali
Other Schools
13:16

Problem 62

In Figure $\mathrm{P} 18.62, R_{1}=0.100 \Omega, R_{2}=1.00 \Omega$, 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 $D$.

Manish Haldankar
Manish Haldankar
Numerade Educator
07:09

Problem 63

What are the expected readings of the ammeter and voltmeter for the circuit in Figure $\mathrm{P} 18.63$ ?

Eduard Sanchez
Eduard Sanchez
Numerade Educator
14:18

Problem 64

Consider the two arrangements of batteries and bulbs shown in Figure P18.64. 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 64 is courtesy of E. F. Redish. For other problems of this type, visit http://www.physics.umd.edu/perg/.)

Manish Haldankar
Manish Haldankar
Numerade Educator
04:12

Problem 65

The given pair of capacitors in Figure $\mathrm{P} 18.65$ are fully charged by a $12.0-\mathrm{V}$ battery. The battery is disconnected and the circuit closed. After $1.00 \mathrm{~ms}$, 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 Ali
Shoukat Ali
Other Schools
02:19

Problem 66

What is the equivalent resistance of the collection of resistors shown in Figure $\mathrm{P} 18.66$ ?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:15

Problem 67

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 $1 \mathrm{~A}$ for about $2.0 \mathrm{~ms}$. Suppose a grown electric eel has $4.0 \times$ $10^{3}$ electrocytes and can deliver up to 300 shocks in rapid series over about 1 s. (a) What maximum electrical power can an electric eel generate? (b) Approximately how much energy does it release in one shock? (c) How high would a mass of $1 \mathrm{~kg}$ have to be lifted so that its gravitational potential energy equals the energy released in 300 such shocks?

Eduard Sanchez
Eduard Sanchez
Numerade Educator