Content check — College Physics (AP), Chapter 20: Electric Current, Resistance, and Ohm's Law

20-1 §20.1 source ↗

What is the current in milliamperes produced by the solar cells of a pocket calculator through which 4.00 C of charge passes in 4.00 h?

Answer

0.278 mA

20-3 §20.1 source ↗

What is the current when a typical static charge of

0.250 μ C

moves from your finger to a metal doorknob in

1.00 μ s

?

Answer

0.250 A

20-5 §20.1 source ↗

A large lightning bolt had a 20,000-A current and moved 30.0 C of charge. What was its duration?

Answer

1.50ms

20-7 §20.1 source ↗

(a) A defibrillator sends a 6.00-A current through the chest of a patient by applying a 10,000-V potential as in the figure below. What is the resistance of the path? (b) The defibrillator paddles make contact with the patient through a conducting gel that greatly reduces the path resistance. Discuss the difficulties that would ensue if a larger voltage were used to produce the same current through the patient, but with the path having perhaps 50 times the resistance. (Hint: The current must be about the same, so a higher voltage would imply greater power. Use this equation for power:

P = I^{2} R

.)

Figure represents a defibrillation unit used on a patient. The circuit is also represented. It shows a capacitor driving a current through the chest of a patient. The opposite plates of the capacitor are marked as positive Q and negative Q. The direction of current in the connecting wires from the capacitor to the defibrillation unit is shown in a clockwise direction with an arrow on the wire, and the direction of electrons is shown opposite to this direction with an arrow. — Figure 20.34 in the book ↗

Answer

(a) $1.67 k Ω$

(b) If a 50 times larger resistance existed, keeping the current about the same, the power would be increased by a factor of about 50 (based on the equation $P = I^{2} R$ ), causing much more energy to be transferred to the skin, which could cause serious burns. The gel used reduces the resistance, and therefore reduces the power transferred to the skin.

20-9 §20.1 source ↗

(a) A defibrillator passes 12.0 A of current through the torso of a person for 0.0100 s. How much charge moves? (b) How many electrons pass through the wires connected to the patient? (See figure two problems earlier.)

Answer

(a) 0.120 C

(b) $7.50 \times 10^{17} electrons$

20-11 §20.1 source ↗

The batteries of a submerged non-nuclear submarine supply 1000 A at full speed ahead. How long does it take to move Avogadro’s number (

6.02 \times 10^{23}

) of electrons at this rate?

Answer

96.3 s

20-13 §20.1 source ↗

A large cyclotron directs a beam of

{He}^{++}

nuclei onto a target with a beam current of 0.250 mA. (a) How many

{He}^{++}

nuclei per second is this? (b) How long does it take for 1.00 C to strike the target? (c) How long before 1.00 mol of

{He}^{++}

nuclei strike the target?

Answer

(a) ${7.81 × 10}^{14} {He}^{++} nuclei/s$

(b) ${4.00 × 10}^{3} s$

(c) ${7.71 × 10}^{8} s$

20-15 §20.1 source ↗

Using the results of the above example on Example 20.3, find the drift velocity in a copper wire of twice the diameter and carrying 20.0 A.

Example 20.3 Calculating Drift Velocity in a Common Wire in the book ↗

Answer

-

1.13 \times 10^{- 4} m/s

20-17 §20.1 source ↗

SPEAR, a storage ring about 72.0 m in diameter at the Stanford Linear Accelerator (closed in 2009), has a 20.0-A circulating beam of electrons that are moving at nearly the speed of light. (See Figure 20.35.) How many electrons are in the beam?

The circuit shows a doughnut shaped storage ring called SPEAR. The cross sections of ring are marked as A and are represented as dotted circular sections. The diameter of storage ring as measured between diametrically opposite cross sections on both ends is seventy two meters. The current in the ring is given as twenty amps. The direction of current I is shown opposite to the direction of movement of electrons e using arrows. — Figure 20.35 in the book ↗

Answer

9.42 \times 10^{13} electrons

20-18 §20.2 source ↗

What current flows through the bulb of a 3.00-V flashlight when its hot resistance is

3 . 60 Ω

?

Answer

0.833 A

20-20 §20.2 source ↗

What is the effective resistance of a car’s starter motor when 150 A flows through it as the car battery applies 11.0 V to the motor?

Answer

7.33 \times 10^{- 2} Ω

20-22 §20.2 source ↗

(a) Find the voltage drop in an extension cord having a

0 . 0600- Ω

resistance and through which 5.00 A is flowing. (b) A cheaper cord utilizes thinner wire and has a resistance of

0.300 Ω

. What is the voltage drop in it when 5.00 A flows? (c) Why is the voltage to whatever appliance is being used reduced by this amount? What is the effect on the appliance?

Answer

(a) 0.300 V

(b) 1.50 V

(c) The voltage supplied to whatever appliance is being used is reduced because the total voltage drop from the wall to the final output of the appliance is fixed. Thus, if the voltage drop across the extension cord is large, the voltage drop across the appliance is significantly decreased, so the power output by the appliance can be significantly decreased, reducing the ability of the appliance to work properly.

20-24 §20.3 source ↗

What is the resistance of a 20.0-m-long piece of 12-gauge copper wire having a 2.053-mm diameter?

Answer

0.104 Ω

20-26 §20.3 source ↗

If the 0.010-mm diameter tungsten filament in a light bulb is to have a resistance of

0.200 Ω

at

20.00º C

, how long should it be?

Answer

2.81 \times 10^{- 4} m

20-28 §20.3 source ↗

What current flows through a 2.54-cm-diameter rod of pure silicon that is 20.0 cm long, when

{1.00 × 10}^{3} V

is applied to it? (Such a rod may be used to make nuclear-particle detectors, for example.)

Answer

1.10 \times 10^{- 3} A

20-30 §20.3 source ↗

A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.00% from its value at

20 . 0º C

. Over what temperature range can it be used?

Answer

- 5º C to 45ºC

20-32 §20.3 source ↗

An electronic device designed to operate at any temperature in the range from

–10 . 0º C to 55 . 0º C

contains pure carbon resistors. By what factor does their resistance increase over this range?

Answer

1.03

20-34 §20.3 source ↗

Assuming a constant temperature coefficient of resistivity, what is the maximum percent decrease in the resistance of a constantan wire starting at

20 . 0º C

?

Answer

0.06%

20-36 §20.3 source ↗

A copper wire has a resistance of

0.500 Ω

at

20 . 0º C

, and an iron wire has a resistance of

0.525 Ω

at the same temperature. At what temperature are their resistances equal?

Answer

- 17º C

20-38 §20.3 source ↗

Integrated Concepts

(a) Redo Exercise 20.25 taking into account the thermal expansion of the tungsten filament. You may assume a thermal expansion coefficient of $12 \times 10^{- 6} / ºC$ . (b) By what percentage does your answer differ from that in the example?

Answer

(a) $4.7 Ω$ (total)

(b) 3.0% decrease

20-40 §20.4 source ↗

What is the power of a

1.00 \times 10^{2} MV

lightning bolt having a current of

{2.00 × 10}^{4} A

?

Answer

2.00 \times 10^{12} W

20-44 §20.4 source ↗

Find the power dissipated in each of these extension cords: (a) an extension cord having a

0 . 0600 - Ω

resistance and through which 5.00 A is flowing; (b) a cheaper cord utilizing thinner wire and with a resistance of

0.300 Ω .

Photograph of a small calculator having a strip of solar cells just above the keys. — Figure 20.36 in the book ↗

Answer

(a) 1.50 W

(b) 7.50 W

20-46 §20.4 source ↗

Show that the units

1 V^{2} / Ω = 1 W

, as implied by the equation

P = V^{2} / R

.

Answer

\frac{V^{2}}{Ω} = \frac{V^{2}}{V/A} = AV = \frac{C}{s} \frac{J}{C} = \frac{J}{s} = 1 W

20-48 §20.4 source ↗

Verify the energy unit equivalence that

1 kW \cdot h = 3 . 60 \times 10^{6} J

.

Answer

1 kW \cdot h= \frac{1 \times 10^{3} J}{1 s} 1 h \frac{3600 s}{1 h} = 3 . 60 \times 10^{6} J

20-50 §20.4 source ↗

An electric water heater consumes 5.00 kW for 2.00 h per day. What is the cost of running it for one year if electricity costs

12.0 cents /kW \cdot h

? See Figure 20.37.

Photograph of an electric hot water heater connected to the electric and water supply — Figure 20.37 in the book ↗

Answer

$438/y

20-52 §20.4 source ↗

What would be the maximum cost of a CFL such that the total cost (investment plus operating) would be the same for both CFL and incandescent 60-W bulbs? Assume the cost of the incandescent bulb is 25 cents and that electricity costs

10 cents/kWh

. Calculate the cost for 1000 hours, as in the cost effectiveness of CFL example.

Answer

$6.25

20-54 §20.4 source ↗

Alkaline batteries have the advantage of putting out constant voltage until very nearly the end of their life. How long will an alkaline battery rated at

1 . 00 A \cdot h

and 1.58 V keep a 1.00-W flashlight bulb burning?

Answer

1.58 h

20-56 §20.4 source ↗

The average television is said to be on 6 hours per day. Estimate the yearly cost of electricity to operate 100 million TVs, assuming their power consumption averages 150 W and the cost of electricity averages

12.0 cents/kW \cdot h

.

Answer

$3.94 billion/year

20-58 §20.4 source ↗

00-gauge copper wire has a diameter of 9.266 mm. Calculate the power loss in a kilometer of such wire when it carries

1.00 \times 10^{2} A

.

Answer

25.5 W

20-60 §20.4 source ↗

Integrated Concepts

(a) What energy is dissipated by a lightning bolt having a 20,000-A current, a voltage of $1.00 \times 10^{2} MV$ , and a length of 1.00 ms? (b) What mass of tree sap could be raised from $18 . 0º C$ to its boiling point and then evaporated by this energy, assuming sap has the same thermal characteristics as water?

Answer

(a) $2.00 \times 10^{9} J$

(b) 769 kg

20-62 §20.4 source ↗

Integrated Concepts

How much time is needed for a surgical cauterizer to raise the temperature of 1.00 g of tissue from $37 . 0º C$ to $100º C$ and then boil away 0.500 g of water, if it puts out 2.00 mA at 15.0 kV? Ignore heat transfer to the surroundings.

Answer

45.0 s

20-64 §20.4 source ↗

Integrated Concepts

(a) Assuming 95.0% efficiency for the conversion of electrical power by the motor, what current must the 12.0-V batteries of a 750-kg electric car be able to supply: (a) To accelerate from rest to 25.0 m/s in 1.00 min? (b) To climb a $2.00 \times 10^{2} -m$ -high hill in 2.00 min at a constant 25.0-m/s speed while exerting $5.00 \times 10^{2} N$ of force to overcome air resistance and friction? (c) To travel at a constant 25.0-m/s speed, exerting a $5.00 \times 10^{2} N$ force to overcome air resistance and friction? See Figure 20.40.

An electric car gets recharged. (credit: “Nissan e-NV200 electric car” by Kārlis Dambrāns, flickr). — Figure 20.40 in the book ↗

Answer

(a) 343 A

(b) $2.17 \times 10^{3} A$

(c) $1.10 \times 10^{3} A$

20-66 §20.4 source ↗

Integrated Concepts

(a) An aluminum power transmission line has a resistance of $0.0580 Ω / km$ . What is its mass per kilometer? (b) What is the mass per kilometer of a copper line having the same resistance? A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.

Answer

(a) $1.23 \times 10^{3} kg$

(b) $2.64 \times 10^{3} kg$

20-69 §20.4 source ↗

Unreasonable Results

(a) What current is needed to transmit $1.00 \times 10^{2} MW$ of power at 480 V? (b) What power is dissipated by the transmission lines if they have a $1 . 00 - Ω$ resistance? (c) What is unreasonable about this result? (d) Which assumptions are unreasonable, or which premises are inconsistent?

Answer

(a) $2.08 \times 10^{5} A$

(b) $4.33 \times 10^{4} MW$

(c) The transmission lines dissipate more power than they are supposed to transmit.

(d) A voltage of 480 V is unreasonably low for a transmission voltage. Long-distance transmission lines are kept at much higher voltages (often hundreds of kilovolts) to reduce power losses.

20-73 §20.5 source ↗

Certain heavy industrial equipment uses AC power that has a peak voltage of 679 V. What is the rms voltage?

Answer

480 V

20-75 §20.5 source ↗

Military aircraft use 400-Hz AC power, because it is possible to design lighter-weight equipment at this higher frequency. What is the time for one complete cycle of this power?

Answer

2.50 ms

20-77 §20.5 source ↗

In this problem, you will verify statements made at the end of the power losses for Example 20.10. (a) What current is needed to transmit 100 MW of power at a voltage of 25.0 kV? (b) Find the power loss in a

1 . 00 - Ω

transmission line. (c) What percent loss does this represent?

Example 20.10 Power Losses Are Less for High-Voltage Transmission in the book ↗

Answer

(a) 4.00 kA

(b) 16.0 MW

(c) 16.0%

20-79 §20.5 source ↗

What is the peak power consumption of a 120-V AC microwave oven that draws 10.0 A?

Answer

2.40 kW

20-81 §20.5 source ↗

Two different electrical devices have the same power consumption, but one is meant to be operated on 120-V AC and the other on 240-V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 120-V AC device is connected to 240-V AC?

Answer

(a) 4.0

(b) 0.50

(c) 4.0

20-83 §20.5 source ↗

Find the time after

t = 0

when the instantaneous voltage of 60-Hz AC first reaches the following values: (a)

V_{0} / 2

(b)

V_{0}

(c) 0.

Answer

(a) 1.39 ms

(b) 4.17 ms

(c) 8.33 ms

20-85 §20.6 source ↗

(a) How much power is dissipated in a short circuit of 220-V AC through a resistance of

0.250 Ω

? (b) What current flows?

Answer

(a) 194 kW

(b) 880 A

20-87 §20.6 source ↗

Find the current through a person and identify the likely effect on her if she touches a 120-V AC source: (a) if she is standing on a rubber mat and offers a total resistance of

300 k Ω

; (b) if she is standing barefoot on wet grass and has a resistance of only

4500 Ω

.

Answer

(a) 0.400 mA, no effect

(b) 26.7 mA, muscular contraction for duration of the shock (can't let go)

20-89 §20.6 source ↗

Foolishly trying to fish a burning piece of bread from a toaster with a metal butter knife, a man comes into contact with 120-V AC. He does not even feel it since, luckily, he is wearing rubber-soled shoes. What is the minimum resistance of the path the current follows through the person?

Answer

1.20 \times 10^{5} Ω

20-91 §20.6 source ↗

(a) What is the resistance of a 220-V AC short circuit that generates a peak power of 96.8 kW? (b) What would the average power be if the voltage was 120 V AC?

Answer

(a) $1.00 Ω$

(b) 14.4 kW

20-93 §20.6 source ↗

Integrated Concepts

A short circuit in a 120-V appliance cord has a $0 . 500 - Ω$ resistance. Calculate the temperature rise of the 2.00 g of surrounding materials, assuming their specific heat capacity is $0.200 cal/g \cdotº C$ and that it takes 0.0500 s for a circuit breaker to interrupt the current. Is this likely to be damaging?

Answer

Temperature increases

860º C

. It is very likely to be damaging.

20-95 §20.7 source ↗

Integrated Concepts

Use the ECG in Figure 20.31 to determine the heart rate in beats per minute assuming a constant time between beats.

This figure has two graphs, placed one below the other. The lower graph shows an E C G of the lead two potential, and the upper graph shows the corresponding changes in arterial blood pressure. In each case, time is plotted on the horizontal axis, in seconds. The vertical axis of the upper graph shows the arterial blood pressure in millimeters of mercury, and the vertical axis of the lower graph shows the lead two voltage in millivolts. The upper graph is roughly sinusoidal, showing the diastolic or minimum blood pressure at about eighty millimeters of mercury, and the systolic or maximum blood pressure at about one hundred twenty millimeters of mercury. For the lower graph, the main features are labeled P, Q, R, S, and T. The P wave is a smooth curve that rises from zero millivolts to a peak of about zero point two five millivolts and falls to just below zero millivolts when it reaches point Q. From point Q to point R, the voltage rises steeply to about one millivolt, and then drops equally sharply to point S, at negative zero point three millivolts. This is followed by the T wave, which is a smooth curve, broader than the P wave, with a peak of comparable height. All of this is completed in less than seven-tenths of a second, with the voltage returning to zero millivolts. After about one-tenth of a second, the cycle begins again. The systolic blood pressure follows soon after the QRS complex. — Figure 20.31 in the book ↗

Answer

80 beats/minute

20-97 §20.7 source ↗

Critical Thinking A copper wire of length 1.25 m is in a circuit. A current of 2.50 A flows through the wire. (a) Initially, the circuit is at

20.0 ° C

. If there is an energy loss of 3.25 MJ in the first second caused by the wire as soon as the circuit is turned on, what is the radius of the wire? (b) After the wire heats

3.000 ° C

, how much energy is being dissipated by the circuit per second? Neglect the effects of thermal expansion since the wire is considered to be physically constrained from expanding. Assume the current is maintained. (c) At what temperature will the energy dissipation be 1.00% higher than it was at the beginning of the experiment?

Answer

(a) $\begin{array}{l} \frac{3.25 \times 10^{- 3}}{1} j/s = P o w e r = I^{2} R = \frac{1}{r^{2}} \frac{{(2.50)}^{2} (1.72 \times 10^{- 8}) (1.25)}{π} {jm}^{2} /s \\ r = \sqrt{\frac{{(2.50)}^{2} (1.72 \times 10^{- 8}) (1.25)}{0.00325 π}} = 3.63 mm \end{array}$

(b) $P o w e r =$ $\frac{{(2.50)}^{2} (1.74 \times 10^{- 8}) (1.25)}{{(3.63 \times 10^{- 3})}^{2} π} j/s$ , so 3.28 j of energy is expended in 1 s. Since $α$ is specified in the chart to only two significant figures, round to 3.3 j.

(c) Since the energy dissipation is directly proportional to the resistivity, the increase of 0.01% in energy dissipation is when the resistivity increases 1%. Or, $1.01 =$ $1 +$ $0.0039 Δ T$ . $T = 23 ° C$ .

AP Test Prep 20.1 §20.1 source ↗

Which of the following can be explained on the basis of conservation of charge in a closed circuit consisting of a battery, resistor, and metal wires?

a.
The number of electrons leaving the battery will be equal to the number of electrons entering the battery.
b.
The number of electrons leaving the battery will be less than the number of electrons entering the battery.
c.
The number of protons leaving the battery will be equal to the number of protons entering the battery.
d.
The number of protons leaving the battery will be less than the number of protons entering the battery.

Answer

A. The number of electrons leaving the battery will be equal to the number of electrons entering the battery.

AP Test Prep 20.3 §20.1 source ↗

If 0.625 × 10²⁰ electrons flow through a circuit each second, what is the current in the circuit?

Answer

10 A

AP Test Prep 20.5 §20.2 source ↗

If the voltage across a fixed resistance is doubled, what happens to the current?

a.
It doubles.
b.
It halves.
c.
It stays the same.
d.
The current cannot be determined.

Answer

A. It doubles.

AP Test Prep 20.7 §20.2 source ↗

What is the resistance of a bulb if the current in it is 1.25 A when a 4 V voltage supply is connected to it? If the voltage supply is increased to 7 V, what will be the current in the bulb?

Answer

3.2 Ω, 2.19 A

AP Test Prep 20.9 §20.3 source ↗

The lengths and diameters of four wires are given as shown.

If the four wires are made from the same material, which of the following is true? Select two answers.

a.
Resistance of Wire 3 > Resistance of Wire 2
b.
Resistance of Wire 1 > Resistance of Wire 2
c.
Resistance of Wire 1 < Resistance of Wire 4
d.
Resistance of Wire 4 < Resistance of Wire 3

The figure shows four cylinders representing sections of wire. The length and diameter of the wires are indicated graphically and with labels below. The wires labeled 2L are the same length and twice as long as the wires labeled L. The wires labeled 2D are twice as thick as the wires labeled D. Wire 1: 2L, D (long, thin). Wire 2: L, D (short, thin). Wire 3: 2L, 2D (long, thick). Wire 4: L, 2D (short, thick). — Figure 20.41 in the book ↗

Answer

B. Resistance of Wire 1 > Resistance of Wire 2 · D. Resistance of Wire 4 < Resistance of Wire 3

AP Test Prep 20.11 §20.3 source ↗

The resistances of two wires having the same lengths and cross section areas are 3 Ω and 11 Ω. If the resistivity of the 3 Ω wire is 2.65 × 10⁻⁸ Ω∙m, find the resistivity of the 1 Ω wire.

Answer

9.72 × 10⁻⁸ Ω∙m

AP Test Prep 20.13 §20.3 source ↗

Suppose the resistance of a wire is 2 Ω. If the wire is stretched to three times its length, what will be its resistance? Assume that the volume does not change.

Answer

18 Ω

AP Test Prep 20.15 §20.4 source ↗

What will be the ratio of the resistance of a 120 W, 220 V lamp to that of a 100 W, 110 V lamp?

Answer

10:3 or 3.33