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College Physics

Hugh D. Young Philip W. Adams

Chapter 19

Current, Resistance, and Direct-Current Circuits - all with Video Answers

Educators


Chapter Questions

03:28

Problem 1

A 5.0 A current flows through the leads of an electrical appliance.
(a) Calculate how much charge passes through the appliance in $1.0 \mathrm{~min} .$ (b) How many electrons are in that amount of charge?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:15

Problem 2

Lightning strikes. During lightning strikes from a cloud to the ground, currents as high as 25,000 A can occur and last for about $40 \mu$ s. How much charge is transferred from the cloud to the earth during such a strike?

Mark J
Mark J
Numerade Educator
02:45

Problem 3

Nerve cells transmit electrical signals through their long tubular axons. These signals propagate due to a sudden rush of $\mathrm{Na}^{+}$ ions, each with charge $+e,$ into the axon. Measurements have revealed that typically about $5.6 \times 10^{11} \mathrm{Na}^{+}$ ions enter each meter of the axon during a time of $10 \mathrm{~ms}$. What is the current during this inflow of charge in a meter of axon?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:34

Problem 4

In an ionic solution, a current consists of $\mathrm{Ca}^{2}+$ ions (of charge $+2 e$ ) and $\mathrm{Cl}^{-}$ ions (of charge $-e$ ) traveling in opposite directions. If $5.11 \times 10^{18} \mathrm{Cl}^{-}$ ions go from $A$ to $B$ every $0.50 \mathrm{~min},$ while $3.24 \times 10^{18} \mathrm{Ca}^{2+}$ ions move from $B$ to $A,$ what is the current (in mA) through this solution, and in which direction (from $A$ to $B$ or from $B$ to $A$ ) is it going?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
04:34

Problem 5

A 14 gauge copper wire of diameter $1.628 \mathrm{~mm}$ carries a current of $12.5 \mathrm{~mA} .$ (a) What is the potential difference across a $2.00 \mathrm{~m}$ length of the wire? (b) What would the potential difference in part (a) be if the wire were silver instead of copper, but all else was the same?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
02:35

Problem 6

You want to precut a set of $1.00 \Omega$ strips of 14 gauge copper wire (of diameter $1.628 \mathrm{~mm}$ ). How long should each strip be?

Yaqub Khan
Yaqub Khan
Numerade Educator
02:58

Problem 7

A wire $6.50 \mathrm{~m}$ long with diameter of $2.05 \mathrm{~mm}$ has a resistance of $0.0290 \Omega .$ What material is the wire most likely made of?

Ryan Kutayiah
Ryan Kutayiah
Texas A&M University
04:55

Problem 8

A tightly coiled spring having 75 coils, each $3.50 \mathrm{~cm}$ in diameter, is made of insulated metal wire $3.25 \mathrm{~mm}$ in diameter. An ohmmeter connected across opposite ends of the spring reads $1.74 \Omega .$ What is the resistivity of the metal?

Yaqub Khan
Yaqub Khan
Numerade Educator
02:21

Problem 9

What diameter must a copper wire have if its resistance is to be the same as that of an equal length of aluminum wire with diameter $3.26 \mathrm{~mm} ?$

Prashant Bana
Prashant Bana
Numerade Educator
05:19

Problem 10

An aluminum bar $3.80 \mathrm{~m}$ long has a rectangular cross section $1.00 \mathrm{~cm}$ by $5.00 \mathrm{~cm} .$ (a) What is its resistance?
(b) What is the length of a copper wire $1.50 \mathrm{~mm}$ in diameter having the same resistance?

Yaqub Khan
Yaqub Khan
Numerade Educator
03:33

Problem 11

A steel wire of length $L$ and radius $r_{1}$ has a resistance $R$. A second steel wire has the same length but a radius $r_{2}$ and a resistance of $3 R$. Find the ratio $r_{1} / r_{2}$

Vishal Gupta
Vishal Gupta
Numerade Educator
04:22

Problem 12

A ductile metal wire has resistance $R$. What will be the resistance of this wire in terms of $R$ if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched? (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)

Yaqub Khan
Yaqub Khan
Numerade Educator
03:19

Problem 13

What is the resistance of a Nichrome wire at $0.0^{\circ} \mathrm{C}$ if its resistance is $100.00 \Omega$ at $11.5^{\circ} \mathrm{C}$ ? The temperature coefficient of resistivity for Nichrome is $0.00040\left(\mathrm{C}^{\circ}\right)^{-1}$

Vishal Gupta
Vishal Gupta
Numerade Educator
08:25

Problem 14

A $1.50 \mathrm{~m}$ cylindrical rod of diameter $0.500 \mathrm{~cm}$ is connected to a power supply that maintains a constant potential difference of $15.0 \mathrm{~V}$ across its ends, while an ammeter measures the current through it. You observe that at room temperature $\left(20.0^{\circ} \mathrm{C}\right)$ the ammeter reads $18.5 \mathrm{~A},$ while at $92.0^{\circ} \mathrm{C}$ it reads $17.2 \mathrm{~A} .$ You can ignore any thermal expansion of the rod. Find (a) the resistivity and (b) the temperature coefficient of resistivity at $20^{\circ} \mathrm{C}$ for the material of the rod.

Yaqub Khan
Yaqub Khan
Numerade Educator
03:22

Problem 15

An iron wire has a temperature coefficient of resistivity of $+0.0050\left(\mathrm{C}^{\circ}\right)^{-1} .$ When it is placed into boiling water, it has a resistance of $1000 \Omega$. What is its resistance when it is placed into an ice-water bath?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:20

Problem 16

In a laboratory experiment, you vary the current through an object and measure the resulting potential difference across it in each case. Figure 19.52 shows a graph of this potential $V$ as a function of the current $I$. (a) Does Ohm's law apply to this object? Why do you say so? (b) How is the resistance of the object related to the slope of the graph? Show why. (c) Use the slope of the graph to find the resistance of the object.

Yaqub Khan
Yaqub Khan
Numerade Educator
06:15

Problem 17

The following measurements of current and potential difference were made on a resistor constructed of Nichrome wire, where $V_{a b}$ is the potential difference across the wire and $I$ is the current through it:
$$\begin{array}{lc}\hline I(\mathrm{~A}) & V_{a b}(\mathrm{~V}) \\\hline 0.50 & 1.94 \\1.00 & 3.88 \\2.00 & 7.76 \\4.00 & 15.52 \\\hline\end{array}$$
(a) Graph $V_{a b}$ as a function of $I$. (b) Does Ohm's law apply to Nichrome? How can you tell? (c) What is the resistance of the resistor in ohms?

Vishal Gupta
Vishal Gupta
Numerade Educator
04:02

Problem 18

When you connect an unknown resistor across the terminals of a 1.50 V AAA battery having negligible internal resistance, you measure a current of 18.0 mA flowing through it. (a) What is the resistance of this resistor? (b) If you now place the resistor across the terminals of a $12.6 \mathrm{~V}$ car battery having no internal resistance, how much current will flow? (c) You now put the resistor across the terminals of an unknown battery of negligible internal resistance and measure a current of 0.453 A flowing through it. What is the potential difference across the terminals of the battery?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:16

Problem 19

The resistance of the body varies from approximately $500 \mathrm{k} \Omega$ (when it is very dry) to about $1 \mathrm{k} \Omega$ (when ?? it is wet). The maximum safe current is about $5.0 \mathrm{~mA}$. At $10 \mathrm{~mA}$ or above, muscle contractions can occur that may be fatal. What is the largest potential difference that a person can safely touch if his body is wet? Is this result within the range of common household voltages?

Yaqub Khan
Yaqub Khan
Numerade Educator
03:20

Problem 20

A copper transmission cable $100 \mathrm{~km}$ long and $10.0 \mathrm{~cm}$ in diameter carries a current of 125 A. What is the potential drop across the cable?

Yaqub Khan
Yaqub Khan
Numerade Educator
01:48

Problem 21

A gold wire $6.40 \mathrm{~m}$ long and of diameter $0.840 \mathrm{~mm}$ carries a current of 1.15 A. Find (a) the resistance of this wire and (b) the potential difference between its ends.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
04:56

Problem 22

A steel wire, of length $L$ and diameter $D,$ has a resistance of $100 \Omega .$ What current would flow through a silver wire of the same diameter and the same length if a $10.0 \mathrm{~V}$ potential difference were applied across its length?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:37

Problem 23

A $6.00 \mathrm{~V}$ lantern battery is connected to a $10.5 \Omega$ lightbulb, and the resulting current in the circuit is 0.350 A. What is the internal resistance of the battery?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
05:53

Problem 24

When the switch in Figure 19.53 is open, the voltmeter $\mathrm{V}$ across the battery reads $3.08 \mathrm{~V}$. When the switch is closed, the voltmeter reading drops to $2.97 \mathrm{~V}$ and the ammeter $\mathrm{A}$ reads 1.65 A. Find the emf, the internal resistance of the battery, and the circuit resistance $R$. Assume that the two meters are ideal, so that they don't affect the circuit.

Vishal Gupta
Vishal Gupta
Numerade Educator
04:51

Problem 25

A nonideal $10.0 \mathrm{~V}$ battery is connected across a resistor $R .$ The internal resistance of the battery is $2.0 \Omega$. Calculate the potential difference across the resistor for the following values: (a) $R=100 \Omega$, (b) $R=10 \Omega,$ (c) $R=2 \Omega$. (d) Find the current through the battery for all three cases.

Vishal Gupta
Vishal Gupta
Numerade Educator
09:39

Problem 26

With a $1500 \mathrm{M} \Omega$ resistor across its terminals, the terminal voltage of a certain battery is $2.50 \mathrm{~V}$. With only a $5.00 \Omega$ resistor across its terminals, the terminal voltage is $1.75 \mathrm{~V}$. (a) Find the internal emf and the internal resistance of this battery. (b) What would be the terminal voltage if the $5.00 \Omega$ resistor were replaced by a $7.00 \Omega$ resistor?

Yaqub Khan
Yaqub Khan
Numerade Educator
01:31

Problem 27

An automobile starter motor is connected to a $12.0 \mathrm{~V}$ battery. When the starter is activated it draws 150 A of current, and the battery voltage drops to $7.0 \mathrm{~V}$. What is the battery's internal resistance?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
02:29

Problem 28

Consider the circuit shown in Figure $19.54 .$ The terminal voltage of the $24.0 \mathrm{~V}$ battery is $21.2 \mathrm{~V}$. What is (a) the internal resistance $r$ of the battery; (b) the resistance $R$ of the circuit resistor?

Yaqub Khan
Yaqub Khan
Numerade Educator
02:17

Problem 29

A resistor with a $15.0 \mathrm{~V}$ potential difference across its ends develops thermal energy at a rate of $327 \mathrm{~W}$. (a) What is the current in the resistor? (b) What is its resistance?

Yaqub Khan
Yaqub Khan
Numerade Educator
02:12

Problem 30

The power rating of a resistor is the maximum power it can safely dissipate without being damaged by overheating. (a) If the power rating of a certain $15 \mathrm{k} \Omega$ resistor is $5.0 \mathrm{~W},$ what is the maximum current it can carry without damage? What is the greatest allowable potential difference across the terminals of this resistor? (b) If a $9.0 \mathrm{k} \Omega$ resistor is to be connected across a $120 \mathrm{~V}$ potential difference, what power rating is required for that resistor?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
03:49

Problem 31

An idealized voltmeter is connected across the terminals of a $15.0 \mathrm{~V}$ battery, and a $75.0 \Omega$ appliance is also connected across its terminals. If the voltmeter reads $11.3 \mathrm{~V}$ : (a) how much power is being dissipated by the appliance, and (b) what is the internal resistance of the battery?

Yaqub Khan
Yaqub Khan
Numerade Educator
00:38

Problem 32

A heart defibrillator is used to enable the heart to start beating if it has stopped. This is done by passing a large current of 12 A through the body at $25 \mathrm{~V}$ for a very short time, usually about $3.0 \mathrm{~ms}$. (a) What power does the defibrillator deliver to the body, and (b) how much energy is transferred?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
02:06

Problem 33

The wattage rating of a lightbulb is the power it consumes when it is connected across a $120 \mathrm{~V}$ potential difference. For example, a $60 \mathrm{~W}$ lightbulb consumes $60.0 \mathrm{~W}$ of electric power only when it is connected across a $120 \mathrm{~V}$ potential difference.
(a) What is the resistance of a $60 \mathrm{~W}$ lightbulb? (b) Without doing any calculations, would you expect a $100 \mathrm{~W}$ bulb to have more or less resistance than a $60 \mathrm{~W}$ bulb? Calculate and find out.

Vishal Gupta
Vishal Gupta
Numerade Educator
04:00

Problem 34

This procedure is not recommended! You'll see why after you work the problem. You are on an aluminum ladder that is standing on the ground, trying to fix an electrical connection with a metal screwdriver that has a metal handle. Your body is wet because you are sweating from the exertion; therefore, it has a resistance of $1.0 \mathrm{k} \Omega .$ (a) If you accidentally touch the "hot" wire connected to the $120 \mathrm{~V}$ line, how much current will pass through your body? Is this amount enough to be dangerous? (The maximum safe current is about $5 \mathrm{~mA} .$ ) (b) How much electric power is delivered to your body?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:41

Problem 35

Electric eels generate electric pulses along their skin that can be used to stun an enemy when they come into contact with it. Tests have shown that these pulses can be up to $500 \mathrm{~V}$ and produce currents of $80 \mathrm{~mA}$ (or even larger). A typical pulse lasts for $10 \mathrm{~ms}$. What power and how much energy are delivered to the unfortunate enemy with a single pulse, assuming a steady current?

Ryan Kutayiah
Ryan Kutayiah
Texas A&M University
05:24

Problem 36

A $500 \Omega$ and a $200 \Omega$ resistor are connected in series with an ideal battery that has an emf of $20 \mathrm{~V}$. (a) What current flows through each resistor? (b) What power is delivered to each resistor? (c) What power is supplied by the battery?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:18

Problem 37

The battery for a certain cell phone is rated at $3.70 \mathrm{~V}$. According to the manufacturer it can produce $3.15 \times 10^{4} \mathrm{~J}$ of electrical energy, enough for 5.25 h of operation, before needing to be recharged. Find the average current that this cell phone draws when turned on.

Yaqub Khan
Yaqub Khan
Numerade Educator
04:49

Problem 38

For the circuit in Figure 19.55 , find (a) the rate of conversion of internal (chemical) energy to electrical energy within the battery, (b) the rate of dissipation of electrical energy in the battery, (c) the rate of dissipation of electrical energy in the external resistor.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:52

Problem 39

A 240 W electric heater is designed to operate from a $12.0 \mathrm{~V}$ car battery. (a) What is its resistance?
(b) What current does it draw? (c) If the battery voltage drops to $11 \mathrm{~V},$ what power does the heater take? (Assume that the resistance is constant.)

Vishal Gupta
Vishal Gupta
Numerade Educator
09:59

Problem 40

Find the equivalent resistance of each combination shown in Figure 19.56.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:05

Problem 41

Calculate the (a) maximum and (b) minimum values of resistance that can be obtained by combining resistors of $36 \Omega, 47 \Omega$, and $51 \Omega$.

Yaqub Khan
Yaqub Khan
Numerade Educator
02:46

Problem 42

Each of two identical uniform metal bars has a resistance $R$.
(a) The end of one bar is welded to the end of the other bar. In terms of $R$, what is the resistance of this combination?
(b) What is the resistance \text { if the bars are welded together along their length? (See Figure 19.57.) }

Vishal Gupta
Vishal Gupta
Numerade Educator
03:55

Problem 43

A $40.0 \Omega$ resistor and a $90.0 \Omega$ resistor are connected in parallel, and the combination is connected across a $120 \mathrm{~V}$ dc line. (a) What is the resistance of the parallel combination? (b) What is the total current through the parallel combination? (c) What is the current through each resistor?

Yaqub Khan
Yaqub Khan
Numerade Educator
07:08

Problem 44

Three resistors having resistances of $1.60 \Omega, 2.40 \Omega,$ and $4.80 \Omega$ are connected in parallel to a $28.0 \mathrm{~V}$ battery that has negligible internal resistance. Find (a) the equivalent resistance of the combination, (b) the current in each resistor, (c) the total current through the battery, (d) the voltage across each resistor, and (e) the power dissipated in each resistor. (f) Which resistor dissipates the most power, the one with the greatest resistance or the one with the least resistance? Explain why this should be.

Vishal Gupta
Vishal Gupta
Numerade Educator
View

Problem 45

Now the three resistors of the previous problem are connected in series to the same battery. Answer the same questions for this situation.

Yaqub Khan
Yaqub Khan
Numerade Educator
02:48

Problem 46

Compute the equivalent resistance of the network in Figure 19.58 , and find the current in each resistor. The battery has negligible internal resistance.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
02:48

Problem 47

Compute the equivalent resistance of the network in Figure 19.59 , and find the current in each resistor. The battery has negligible internal resistance.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
02:32

Problem 48

The power rating of a lightbulb is the power it consumes when connected across a $120 \mathrm{~V}$ outlet. (a) If you put two $100 \mathrm{~W}$ bulbs in series across a $120 \mathrm{~V}$ outlet, how much power would each consume if its resistance were constant? (b) How much power does each one consume if you connect them in parallel across a $120 \mathrm{~V}$ outlet?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:53

Problem 49

You have two $10 \Omega$ resistors and one $40 \Omega$ resistor. What combination of these will produce an equivalent resistance of (a) $45 \Omega$,
(b) $18 \Omega,(\mathrm{c}) 4.44 \Omega ?$
19.6 Kirchhoff's Rules

Vishal Gupta
Vishal Gupta
Numerade Educator
03:01

Problem 50

The batteries shown in the circuit in Figure 19.60 have negligibly small internal resistances. Find the current through (a) the $30.0 \Omega$ resistor, (b) the $20.0 \Omega$ resistor, and (c) the $10.0 \mathrm{~V}$ battery.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
04:11

Problem 51

Find the emf's $\mathcal{E}_{1}$ and $\mathcal{E}_{2}$ in the circuit shown in Figure 19.61 .

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
07:38

Problem 52

For the circuit shown in Figure $19.62,$ calculate (a) the resistance of $R,$ (b) the current through the $40 \Omega$ resistor, and (c) the power supplied by the $160 \mathrm{~V}$ battery. (Assume that the batteries have no internal resistance.)

Christopher Dzorkpata
Christopher Dzorkpata
Numerade Educator
03:04

Problem 53

In the circuit shown in Figure 19.63 , find (a) the current in resistor $R,$ (b) the value of the resistance $R,$ and (c) the unknown emf $\mathcal{E}$.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
04:23

Problem 54

In the circuit shown in Figure $19.64,$ current flows through the $5.00 \Omega$ resistor in the direction shown, and this resistor is measured to be consuming energy at a rate of $20.0 \mathrm{~W}$. The batteries have negligibly small internal resistance. What current does the ammeter A read?

Yaqub Khan
Yaqub Khan
Numerade Educator
07:04

Problem 55

In the circuit shown in Figure 19.65 , the $6.0 \Omega$ resistor is consuming energy at a rate of $24 \mathrm{~J} / \mathrm{s}$ when the current through it flows as shown.
(a) Find the current through the ammeter A. (b) What are the polarity and $\mathrm{emf} \mathcal{E}$ of the battery, assuming it has negligible internal resistance?

Christopher Dzorkpata
Christopher Dzorkpata
Numerade Educator
01:28

Problem 56

A $500.0 \Omega$ resistor is connected in series with a capacitor. What must be the capacitance of the capacitor to produce a time constant of $2.00 \mathrm{~s} ?$

Yaqub Khan
Yaqub Khan
Numerade Educator
01:51

Problem 57

A fully charged $6.0 \mu \mathrm{F}$ capacitor is connected in series with a $1.5 \times 10^{5} \Omega$ resistor. What percentage of the original charge is left on the capacitor after 1.8 s of discharging?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
15:52

Problem 58

A $12.4 \mu \mathrm{F}$ capacitor is connected through a $0.895 \mathrm{M} \Omega$ resistor to a constant potential difference of $60.0 \mathrm{~V}$. (a) Compute the charge on the capacitor at the following times after the connections are made:
$0,5.0 \mathrm{~s}, 10.0 \mathrm{~s}, 20.0 \mathrm{~s},$ and $100.0 \mathrm{~s} .$ (b) Compute the charging currents at the same instants. (c) Graph the results of parts (a) and (b) for $t$ between 0 and $20 \mathrm{~s}$

Yaqub Khan
Yaqub Khan
Numerade Educator
06:22

Problem 59

A $6.00 \mu \mathrm{F}$ capacitor that is initially uncharged is connected in series with a $4500 \Omega$ resistor and a $500 \mathrm{~V}$ emf source with negligible internal resistance. Just after the circuit is completed, what are (a) the voltage drop across the capacitor, (b) the voltage drop across the resistor, (c) the charge on the capacitor, and (d) the current through the resistor? (e) A long time after the circuit is completed (after many time constants), what are the values of the preceding four quantities?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
03:16

Problem 60

A capacitor is charged to a potential of $12.0 \mathrm{~V}$ and is then connected to a voltmeter having an internal resistance of $3.40 \mathrm{M} \Omega$. After a time of $4.00 \mathrm{~s}$, the voltmeter reads $3.0 \mathrm{~V}$. What are (a) the capacitance and (b) the time constant of the circuit?

Shital Rijal
Shital Rijal
Numerade Educator
04:18

Problem 61

A $1.0 \mu \mathrm{F}$ capacitor is being charged by a $9.0 \mathrm{~V}$ battery through a $10 \mathrm{M} \Omega$ resistor. Determine the potential across the capacitor at times (a) $t=1.0 \mathrm{~s},$ (b) $t=5.0 \mathrm{~s},$ and
(c) $t=20 \mathrm{~s}$

Vishal Gupta
Vishal Gupta
Numerade Educator
09:25

Problem 62

In the circuit shown in Figure 19.66 , the capacitors are all initially uncharged and the battery has no appreciable internal resistance. After the switch is closed, find (a) the maximum charge on each capacitor, (b) the maximum potential difference across each capacitor, (c) the maximum reading of the ammeter $\mathrm{A},$ and (d) the time constant for the circuit.

Vishal Gupta
Vishal Gupta
Numerade Educator
07:02

Problem 63

A $1.50 \mu \mathrm{F}$ capacitor is charged through a $125 \Omega$ resistor and then discharged through the same resistor by short-circuiting the battery. While the capacitor is being charged, find (a) the time for the charge on its plates to reach $1-1 / e$ of its maximum value and $(b)$ the current in the circuit at that time. (c) During the discharge of the capacitor, find the time for the charge on its plates to decrease to $1 / e$ of its initial value. Also, find the time for the current in the circuit to decrease to $1 / e$ of its initial value.

Vishal Gupta
Vishal Gupta
Numerade Educator
14:38

Problem 64

An initially uncharged capacitor $C$ charges through a resistor $R$ for many time constants and then discharges through the same resistor. Call $Q_{\max }$ the maximum charge on its plates and $I_{\max }$ the maximum current in the circuit. (a) Sketch clear graphs of the charge on the plates and the current in the circuit as functions of time for the charging process. (b) During the discharging process, the charge on the capacitor and the current both decrease exponentially from their maximum values. Use this fact to sketch graphs of the current in the circuit and the charge on the capacitor as functions of time.

Yaqub Khan
Yaqub Khan
Numerade Educator
04:19

Problem 65

The circuit shown in Figure 19.67 contains two batteries, each with an emf and an internal resistance, and two resistors. Find (a) the current in the circuit (magnitude and direction) and (b) the terminal voltage $V_{a b}$ of the $16.0 \mathrm{~V}$ battery.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
12:58

Problem 66

If an ohmmeter is connected between points $a$ and $b$ in each of the circuits shown in Figure $19.68,$ what will it read?

Yaqub Khan
Yaqub Khan
Numerade Educator
02:45

Problem 67

A refrigerator draws 3.5 A of current while operating on a $120 \mathrm{~V}$ power line. If the refrigerator runs $50 \%$ of the time and electric power costs $\$ 0.12$ per $\mathrm{kWh}$, how much does it cost to run this refrigerator for a 30 -day month?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
05:41

Problem 68

A toaster using a Nichrome heating element operates on $120 \mathrm{~V}$. When it is switched on at $20^{\circ} \mathrm{C}$, the heating element carries an initial current of 1.35 A. A few seconds later, the current reaches the steady value of 1.23 A. (a) What is the final temperature of the element? The average value of the temperature coefficient of resistivity for Nichrome over the temperature range from $20^{\circ} \mathrm{C}$ to the final temperature of the element is $4.5 \times 10^{-4}\left(\mathrm{C}^{\circ}\right)^{-1} .$ (b) What is the power dissipated in the heating element (i) initially; (ii) when the current reaches a steady value?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:23

Problem 69

A piece of wire has a resistance $R$. It is cut into three pieces of equal length, and the pieces are twisted together parallel to each other. What is the resistance of the resulting wire in terms of $R ?$

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
08:05

Problem 70

A typical small flashlight contains two batteries, each having an emf of $1.5 \mathrm{~V},$ connected in series with a bulb having resistance $17 \Omega$. (a) If the internal resistance of the batteries is negligible, what power is delivered to the bulb? (b) If the batteries last for $5.0 \mathrm{~h}$, what is the total energy delivered to the bulb? (c) The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial value? (Assume that the resistance of the bulb is constant. Actually, it will change somewhat when the current through the filament changes because this changes the temperature of the filament and hence the resistivity of the filament wire.

Ryan Kutayiah
Ryan Kutayiah
Texas A&M University
06:00

Problem 71

In the circuit of Figure $19.69,$ find (a) the current through the $8.0 \Omega$ resistor, (b) the total rate of dissipation of electrical energy in the $8.0 \Omega$ resistor and in the internal resistance of the batteries, and
(c) the total power being delivered by the two batteries.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:15

Problem 72

Lightning strikes can involve currents as high as 25,000 A that last for about $40 \mu$ s. If a person is struck by a bolt of lightning with these properties, the current will pass through his body. We shall assume that his mass is $75 \mathrm{~kg},$ that he is wet (after all, he is in a rainstorm) and therefore has a resistance of $1.0 \mathrm{k} \Omega$, and that his body is all water (which is reasonable for a rough, but plausible, approximation).
(a) By how many degrees Celsius would this lightning bolt increase the temperature of 75 kg of water? (b) Given that the internal body temperature is about $37^{\circ} \mathrm{C},$ would the person's temperature actually increase that much? Why or why not? What would happen first?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
04:58

Problem 73

Each of the three resistors in Figure 19.70 has a resistance of $2.00 \Omega$ and can dissipate a maximum of $32.0 \mathrm{~W}$ without becoming excessively heated. What is the maximum power the circuit can dissipate?

Yaqub Khan
Yaqub Khan
Numerade Educator
04:31

Problem 74

An $1800 \mathrm{~W}$ toaster, a $1400 \mathrm{~W}$ electric frying pan, and a 75 W lamp are plugged into the same electrical outlet in a $20 \mathrm{~A}, 120 \mathrm{~V}$ circuit. (Note: When plugged into the same outlet, the three devices are in parallel with each other across the $120 \mathrm{~V}$ outlet. $)$ (a) What current is drawn by each device?
(b) Will this combination blow the circuit breaker?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:09

Problem 75

Two identical $1.00 \Omega$ wires are laid side by side and soldered together so that they touch each other for half of their lengths. (See Figure $19.71 .)$ What is the equivalent resistance of this combination?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
04:59

Problem 76

Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. What power would be dissipated if the three resistors were connected in parallel across the same potential difference?

Yaqub Khan
Yaqub Khan
Numerade Educator
08:15

Problem 77

(a) Calculate the equivalent resistance of the circuit of Figure 19.72 between $x$ and $y$
(b) If a voltmeter is connected between points $a$ and $x$ when the current in the $8.0 \Omega$ resistor is 2.4 A in the direction from left to right in the figure, what will it read?

Vishal Gupta
Vishal Gupta
Numerade Educator
07:25

Problem 78

A power plant transmits $150 \mathrm{~kW}$ of power to a nearby town through wires that have a total resistance of $0.25 \Omega$. What percentage of the power is dissipated as heat in the wire if the power is transmitted at (a) $220 \mathrm{~V}$ and
(b) $22 \mathrm{kV} ?$

Yaqub Khan
Yaqub Khan
Numerade Educator
02:04

Problem 79

What must the emf $\mathcal{E}$ in Figure 19.73 be in order for the current through the $7.00 \Omega$ resistor to be 1.80 A? Each emf source has negligible internal resistance.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
13:01

Problem 80

For the circuit shown in Figure $19.74,$ if a voltmeter is connected across points $a$ and $b$, (a) what will it read, and (b) which point is at a higher potential, $a$ or $b ?$

Yaqub Khan
Yaqub Khan
Numerade Educator
03:20

Problem 81

A $4600 \Omega$ resistor is connected across a charged $0.800 \mathrm{nF}$ capacitor. The initial current through the resistor, just after the connection is made, is measured to be $0.250 \mathrm{~A}$. (a) What magnitude of charge was initially on each plate of this capacitor? (b) How long after the connection is made will it take before the charge is reduced to $1 / e$ of its maximum value?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
02:04

Problem 82

A capacitor that is initially uncharged is connected in series with a resistor and a $400.0 \mathrm{~V}$ emf source with negligible internal resistance. Just after the circuit is completed, the current through the resistor is $0.800 \mathrm{~mA}$ and the time constant for the circuit is $6.00 \mathrm{~s}$ What are (a) the resistance of the resistor and (b) the capacitance of the capacitor?

Yaqub Khan
Yaqub Khan
Numerade Educator
04:24

Problem 83

In the circuit shown in Figure $19.75, R$ is a variable resistor whose value can range from 0 to $\infty,$ and $a$ and $b$ are the terminals of a battery having an emf $\mathcal{E}=15.0 \mathrm{~V}$ and an internal resistance of $4.00 \Omega .$ The ammeter and voltmeter are both idealized meters. As $R$ varies over its full range of values, what will be the largest and smallest readings of (a) the voltmeter and (b) the ammeter? (c) Sketch qualitative graphs of the readings of both meters as functions of $R,$ as $R$ ranges from 0 to $\infty$.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
04:41

Problem 84

Some types of spiders build webs that consist of threads made of dry silk coated with a solution of a variety of compounds. This coating leaves the threads, which are used to capture prey, hygroscopic-that is, they attract water from the atmosphere. It has been hypothesized that this aqueous coating makes the threads good electrical conductors. To test the electrical properties of coated thread, researchers placed a $5 \mathrm{~mm}$ length of thread between two electrical contacts. The researchers stretched the thread in $1 \mathrm{~mm}$ increments to more than twice its original length, and then allowed it to return to its original length, again in $1 \mathrm{~mm}$ increments. Some of the resistance measurements are given in the table:
$$\begin{array}{l|cccccccc}\begin{array}{l}\text { Resistance of } \\\text { thread }\left(10^{9} \Omega\right)\end{array} & 9 & 19 & 41 & 63 & 102 & 76 & 50 & 24 \\
\hline \begin{array}{l}\text { Length of } \\\text { thread }(\mathrm{mm})\end{array} & 5 & 7 & 9 & 11 & 13 & 9 & 7 & 5\end{array}$$
What is the best explanation for the behavior exhibited in the data?
A. Longer threads can carry more current than shorter threads and so make better electrical conductors.
B. The thread stops being a conductor when it is stretched to 13 $\mathrm{mm}$ due to breaks that occur in the thin coating.
C. As the thread is stretched, the coating thins and its resistance increases; as the thread is relaxed, the coating returns nearly to its original state.
D. The resistance of the thread increases with distance from the end of the thread.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:30

Problem 85

Some types of spiders build webs that consist of threads made of dry silk coated with a solution of a variety of compounds. This coating leaves the threads, which are used to capture prey, hygroscopic-that is, they attract water from the atmosphere. It has been hypothesized that this aqueous coating makes the threads good electrical conductors. To test the electrical properties of coated thread, researchers placed a $5 \mathrm{~mm}$ length of thread between two electrical contacts. The researchers stretched the thread in $1 \mathrm{~mm}$ increments to more than twice its original length, and then allowed it to return to its original length, again in $1 \mathrm{~mm}$ increments. Some of the resistance measurements are given in the table:
$$\begin{array}{l|cccccccc}\begin{array}{l}\text { Resistance of } \\\text { thread }\left(10^{9} \Omega\right)\end{array} & 9 & 19 & 41 & 63 & 102 & 76 & 50 & 24 \\
\hline \begin{array}{l}\text { Length of } \\\text { thread }(\mathrm{mm})\end{array} & 5 & 7 & 9 & 11 & 13 & 9 & 7 & 5\end{array}$$

If the conductivity of the thread results from the aqueous coating only, how does the cross-sectional area $A$ of the coating compare when the thread is $13 \mathrm{~mm}$ long versus the starting length of $5 \mathrm{~mm} ?$ Assume that the resistivity of the coating remains constant and the coating is uniform along the thread. $A_{13 \mathrm{~mm}}$ is about
A. $1 / 10 A_{5 \mathrm{~mm}}$
B. $1 / 4 A_{5 \mathrm{~mm}}$
C. $2.5 \mathrm{~A}_{5 \mathrm{~mm}}$
D. the same as $A_{5 \mathrm{~mm}}$

Vishal Gupta
Vishal Gupta
Numerade Educator
02:03

Problem 86

Some types of spiders build webs that consist of threads made of dry silk coated with a solution of a variety of compounds. This coating leaves the threads, which are used to capture prey, hygroscopic-that is, they attract water from the atmosphere. It has been hypothesized that this aqueous coating makes the threads good electrical conductors. To test the electrical properties of coated thread, researchers placed a $5 \mathrm{~mm}$ length of thread between two electrical contacts. The researchers stretched the thread in $1 \mathrm{~mm}$ increments to more than twice its original length, and then allowed it to return to its original length, again in $1 \mathrm{~mm}$ increments. Some of the resistance measurements are given in the table:
$$\begin{array}{l|cccccccc}\begin{array}{l}\text { Resistance of } \\\text { thread }\left(10^{9} \Omega\right)\end{array} & 9 & 19 & 41 & 63 & 102 & 76 & 50 & 24 \\
\hline \begin{array}{l}\text { Length of } \\\text { thread }(\mathrm{mm})\end{array} & 5 & 7 & 9 & 11 & 13 & 9 & 7 & 5\end{array}$$

What is the maximum current that flows in the thread during this experiment if the voltage source is a $9 \mathrm{~V}$ battery?
A. about $1 A$
B. about $0.1 A$
C. about $1 \mu A$
D. about 1 nA

Vishal Gupta
Vishal Gupta
Numerade Educator
03:20

Problem 87

Some types of spiders build webs that consist of threads made of dry silk coated with a solution of a variety of compounds. This coating leaves the threads, which are used to capture prey, hygroscopic-that is, they attract water from the atmosphere. It has been hypothesized that this aqueous coating makes the threads good electrical conductors. To test the electrical properties of coated thread, researchers placed a $5 \mathrm{~mm}$ length of thread between two electrical contacts. The researchers stretched the thread in $1 \mathrm{~mm}$ increments to more than twice its original length, and then allowed it to return to its original length, again in $1 \mathrm{~mm}$ increments. Some of the resistance measurements are given in the table:
$$\begin{array}{l|cccccccc}\begin{array}{l}\text { Resistance of } \\\text { thread }\left(10^{9} \Omega\right)\end{array} & 9 & 19 & 41 & 63 & 102 & 76 & 50 & 24 \\
\hline \begin{array}{l}\text { Length of } \\\text { thread }(\mathrm{mm})\end{array} & 5 & 7 & 9 & 11 & 13 & 9 & 7 & 5\end{array}$$

In another experiment, a piece of the web is suspended so that it can move freely. When either a positively charged object or a negatively charged object is brought near the web, the thread is observed to move toward the charged object. What is the best interpretation of this observation? The web is
A. a negatively charged conductor.
B. a positively charged conductor.
C. either a positively or negatively charged conductor.
D. an electrically neutral conductor.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:14

Problem 88

The portion of a nerve cell that conducts signals is called an axon. Many of the electrical properties of axons are governed by ion channels, which are protein molecules that span the axon's cell membrane. When open, each ion channel has a pore that is filled with fluid of low resistivity and connects the interior of the cell electrically to the medium outside the cell. In contrast, the lipid-rich cell membrane in which ion channels reside has very high resistivity.

Assume that a typical open ion channel spanning an axon's membrane has a resistance of $1 \times 10^{11} \Omega .$ We can model this ion channel, with its pore, as a 12 -nm-long cylinder of radius $0.3 \mathrm{nm}$. What is the resistivity of the fluid in the pore? A. $10 \Omega \cdot \mathrm{m}$
B. $6 \Omega \cdot \mathrm{m}$
C. $2 \Omega \cdot \mathrm{m}$
D. $1 \Omega \cdot \mathrm{m}$

Vishal Gupta
Vishal Gupta
Numerade Educator
02:14

Problem 89

The portion of a nerve cell that conducts signals is called an axon. Many of the electrical properties of axons are governed by ion channels, which are protein molecules that span the axon's cell membrane. When open, each ion channel has a pore that is filled with fluid of low resistivity and connects the interior of the cell electrically to the medium outside the cell. In contrast, the lipid-rich cell membrane in which ion channels reside has very high resistivity.

In a simple model of an axon conducting a nerve signal, ions move across the cell membrane through open ion channels, which act as purely resistive elements. If a typical current density (current per unit cross-sectional area) in the cell membrane is $5 \mathrm{~mA} / \mathrm{cm}^{2}$ when the voltage across the membrane (the action potential) is $50 \mathrm{mV}$, what is the number density of open ion channels in the membrane?
A. $1 / \mathrm{cm}^{2}$
B. $10 / \mathrm{cm}^{2}$
C. $10 / \mathrm{mm}^{2}$
D. $100 / \mu \mathrm{m}^{2}$

Vishal Gupta
Vishal Gupta
Numerade Educator
02:14

Problem 90

The portion of a nerve cell that conducts signals is called an axon. Many of the electrical properties of axons are governed by ion channels, which are protein molecules that span the axon's cell membrane. When open, each ion channel has a pore that is filled with fluid of low resistivity and connects the interior of the cell electrically to the medium outside the cell. In contrast, the lipid-rich cell membrane in which ion channels reside has very high resistivity.

Cell membranes across a wide variety of organisms have a capacitance per unit area of $1 \mu \mathrm{F} / \mathrm{cm}^{2} .$ For the electrical signal in a nerve to propagate down the axon, the charge on the membrane "capacitor" must change. What time constant is required when the ion channels are open?
A. $1 \mu$ s
B. $10 \mu$ s
C. $100 \mu \mathrm{s}$
D. $1 \mathrm{~ms}$

Vishal Gupta
Vishal Gupta
Numerade Educator