College Physics for AP® Courses

Irina Lyublinskaya, Gregg Wolfe, Douglas Ingram , Liza Pujji

Chapter 20

Electric Current, Resistance, and Ohm's Law - all with Video Answers

Educators

Chapter Questions

Problem 1

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?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 2

A total of 600 C of charge passes through a flashlight in 0.500 h. What is the average current?

Ze-Han Lee

Numerade Educator

Problem 3

What is the current when a typical static charge of 0.250$\mu C$ moves from your finger to a metal doorknob in 1.00$\mu \mathrm{s} ?$

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 4

Find the current when 2.00 $\mathrm{nC}$ jumps between your comb and hair over a $0.500-\mu \mathrm{s}$ time interval.

Ze-Han Lee

Numerade Educator

Problem 5

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

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 6

The 200-A current through a spark plug moves 0.300 mC of charge. How long does the spark last?

Ze-Han Lee

Numerade Educator

Problem 7

(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: $P=I^{2} R$ ).

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 8

During open-heart surgery, a defibrillator can be used to bring a patient out of cardiac arrest. The resistance of the path is 500$\Omega$ and a 10.0 -mA current is needed. What voltage should be applied?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 9

(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.)

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 10

A clock battery wears out after moving 10,000 C of charge through the clock at a rate of 0.500 mA. (a) How long did the clock run? (b) How many electrons per second flowed?

Ze-Han Lee

Numerade Educator

Problem 11

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 ( 6.02×1023 ) of electrons at this rate?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 12

Electron guns are used in X-ray tubes. The electrons are accelerated through a relatively large voltage and directed onto a metal target, producing X-rays. (a) How many electrons per second strike the target if the current is 0.500 mA? (b) What charge strikes the target in 0.750 s?

Ze-Han Lee

Numerade Educator

Problem 13

A large cyclotron directs a beam of $\mathrm{He}^{++}$ nuclei onto a target with a beam current of 0.250 $\mathrm{mA}$ . (a) How many $\mathrm{He}^{++}$ nuclei per second is this? (b) How long does it take for 1.00 $\mathrm{C}$ to strike the target? (c) How long before 1.00 $\mathrm{mol}$ of $\mathrm{He}^{++}$ nuclei strike the target?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 14

Repeat the above example on Example 20.3, but for a wire made of silver and given there is one free electron per silver atom.

Ren Jie Tuieng

Numerade Educator

Problem 15

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.

Ren Jie Tuieng

Numerade Educator

Problem 16

A 14-gauge copper wire has a diameter of 1.628 mm. What magnitude current flows when the drift velocity is 1.00 mm/s? (See above example on Example 20.3 for useful information.)

Ze-Han Lee

Numerade Educator

Problem 17

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 20.42.) How many electrons are in the beam?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 18

What current flows through the bulb of a 3.00 -V flashlight when its hot resistance is 3.60$\Omega ?$

Ze-Han Lee

Numerade Educator

Problem 19

Calculate the effective resistance of a pocket calculator that has a 1.35-V battery and through which 0.200 mA flows.

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 20

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?

Ze-Han Lee

Numerade Educator

Problem 21

How many volts are supplied to operate an indicator light on a DVD player that has a resistance of 140 ? , given that 25.0 mA passes through it?

Keshav Singh

Numerade Educator

Problem 22

(a) Find the voltage drop in an extension cord having a $0.0600-\Omega$ resistance and through which 5.00 a is flowing. (b) A cheaper cord utilizes thinner wire and has a resistance of 0.300 \Omega. What is the voltage drop in it when 5.00 $\mathrm{A}$ flows? (c) Why is the voltage to whatever appliance is being used reduced by this amount? What is the effect on the appliance?

Ze-Han Lee

Numerade Educator

Problem 23

A power transmission line is hung from metal towers with glass insulators having a resistance of $1.00 \times 10^{9}$ . What current flows through the insulator if the voltage is 200 $\mathrm{kV}$ ? (Some high-voltage lines are DC.)

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 24

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

Ze-Han Lee

Numerade Educator

Problem 25

The diameter of 0-gauge copper wire is 8.252 mm. Find the resistance of a 1.00-km length of such wire used for power transmission.

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 26

If the 0.100 -mm diameter tungsten filament in a light bulb is to have a resistance of 0.200$\Omega$ at $20.0^{\circ} \mathrm{C},$ how long should it be?

Ze-Han Lee

Numerade Educator

Problem 27

Find the ratio of the diameter of aluminum to copper wire, if they have the same resistance per unit length (as they might in household wiring).

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 28

What current flows through a 2.54 -cm-diameter rod of pure silicon that is 20.0 $\mathrm{cm}$ long, when $1.00 \times 10^{3} \mathrm{V}$ is applied to it? (Such a rod may be used to make nuclear-particle detectors, for example.)

Ze-Han Lee

Numerade Educator

Problem 29

(a) To what temperature must you raise a copper wire, originally at $20.0^{\circ} \mathrm{C}$ , to double its resistance, neglecting any changes in dimensions? (b) Does this happen in household wiring under ordinary circumstances?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 30

A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.00$\%$ from its value at $20.0^{\circ} \mathrm{C}$ . Over what temperature range can it be used?

Ze-Han Lee

Numerade Educator

Problem 31

Of what material is a resistor made if its resistance is 40.0$\%$ greater at $100^{\circ} \mathrm{C}$ than at $20.0^{\circ} \mathrm{C} ?$

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 32

An electronic device designed to operate at any temperature in the range from $-10.0^{\circ} \mathrm{C}$ to $55.0^{\circ} \mathrm{C}$ contains pure carbon resistors. By what factor does their resistance increase over this range?

Ze-Han Lee

Numerade Educator

Problem 33

(a) Of what material is a wire made, if it is 25.0 $\mathrm{m}$ long with a 0.100 $\mathrm{mm}$ diameter and has a resistance of 77.7 ? $\Omega$ at $20.0^{\circ} \mathrm{C} ?$ (b) What is its resistance at $150^{\circ} \mathrm{C} ?$

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 34

Assuming a constant temperature coefficient of resistivity, what is the maximum percent decrease in the resistance of a constantan wire starting at $20.0^{\circ} \mathrm{C} ?$

Ze-Han Lee

Numerade Educator

Problem 35

A wire is drawn through a die, stretching it to four times its original length. By what factor does its resistance increase?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 36

A copper wire has a resistance of 0.500$\Omega$ at $20.0^{\circ} \mathrm{C}$ and an iron wire has a resistance of 0.525$\Omega$ at the same temperature. At what temperature are their resistances equal?

Ze-Han Lee

Numerade Educator

Problem 37

(a) Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has $\alpha=-0.0600 /^{\circ} \mathrm{C}$ ) when it is at the same temperature as the patient. What is a patient's temperature if the thermistor's resistance at that temperature is 82.0$\%$ of its value at $37.0^{\circ} \mathrm{C}$ (normal body temperature)? (b) The negative value for $\alpha$ may not be maintained for very low temperatures. Discuss why and whether this is the case here. (Hint: Resistance can't become negative.)

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 38

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 $12 \times 10^{-6} /^{\circ} \mathrm{C}$ . b ) By what percentage does your answer differ from that in the example?

Alex Breitweiser

Alex Breitweiser

Numerade Educator

Problem 39

Unreasonable Results
(a) To what temperature must you raise a resistor made of constantan to double its resistance, assuming a constant temperature coefficient of resistivity? (b) To cut it in half? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable, or which premises are inconsistent?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 40

What is the power of a $1.00 \times 10^{2} \mathrm{MV}$ lighthing bolt having a current of $2.00 \times 10^{4} \mathrm{A} ?$

Ze-Han Lee

Numerade Educator

Problem 41

What power is supplied to the starter motor of a large truck that draws 250 A of current from a 24.0-V battery hookup?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 42

A charge of 4.00 C of charge passes through a pocket calculator's solar cells in 4.00 h. What is the power output, given the calculator's voltage output is 3.00 V? (See Figure 20.43.)

Ze-Han Lee

Numerade Educator

Problem 43

How many watts does a flashlight that has $6.00 \times 10^{2} \mathrm{C}$ pass through it in 0.500 h use if its voltage is 3.00 $\mathrm{V} ?$

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 44

Find the power dissipated in each of these extension cords: (a) an extension cord having a $0.0600-\Omega$ resistance and through which 5.00 A is flowing; (b) a cheaper cord utilizing thinner wire and with a resistance of 0.300$\Omega .$

Ze-Han Lee

Numerade Educator

Problem 45

Verify that the units of a volt-ampere are watts, as implied by the equation $P=I V$

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 46

Show that the units $1 \mathrm{V}^{2} / \Omega=1 \mathrm{W}$ , as implied by the equation $P=V^{2} / R$

Ze-Han Lee

Numerade Educator

Problem 47

Show that the units $1 \mathrm{A}^{2} \cdot \Omega=1 \mathrm{W},$ as implied by the equation $P=I^{2} R$

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 48

Verify the energy unit equivalence that $1 \mathrm{kW} \cdot \mathrm{h}=3.60 \times 10^{6} \mathrm{J}$

Ze-Han Lee

Numerade Educator

Problem 49

Electrons in an $X$ -ray tube are accelerated through $1.00 \times 10^{2} \mathrm{kV}$ and directed toward a target to produce $\mathrm{X}$ - rays. Calculate the power of the electron beam in this tube if it has a current of 15.0 $\mathrm{mA} .$

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 50

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 ? h ? See Figure 20.44.

Ze-Han Lee

Numerade Educator

Problem 51

With a 1200-W toaster, how much electrical energy is needed to make a slice of toast (cooking time = 1 minute)? At 9.0 cents/kW · h , how much does this cost?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 52

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.

Ze-Han Lee

Numerade Educator

Problem 53

Some makes of older cars have 6.00-V electrical systems. (a) What is the hot resistance of a 30.0-W headlight in such a car? (b) What current flows through it?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 54

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

Ze-Han Lee

Numerade Educator

Problem 55

A cauterizer, used to stop bleeding in surgery, puts out 2.00 mA at 15.0 kV. (a) What is its power output? (b) What is the resistance of the path?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 56

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 ? h .

Ze-Han Lee

Numerade Educator

Problem 57

An old lightbulb draws only 50.0 W, rather than its original 60.0 W, due to evaporative thinning of its filament. By what factor is its diameter reduced, assuming uniform thinning along its length? Neglect any effects caused by temperature differences.

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 58

00 -gauge copper wire has a diameter of 9.266 $\mathrm{mm}$ . Calculate the power loss in a kilometer of such wire when it carries $1.00 \times 10^{2} \mathrm{A}$ .

Ze-Han Lee

Numerade Educator

Problem 59

Integrated Concepts
Cold vaporizers pass a current through water, evaporating it with only a small increase in temperature. One such home device is rated at 3.50 A and utilizes 120 V AC with 95.0% efficiency. (a) What is the vaporization rate in grams per minute? (b) How much water must you put into the vaporizer for 8.00 h of overnight operation? (See Figure 20.45.)

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 60

Integrated Concepts
(a) What energy is dissipated by a lightning bolt having a $20,000$ -A current, a voltage of $1.00 \times 10^{2} \mathrm{MV}$ , and a length of 1.00 $\mathrm{ms}$ (b) What mass of tree sap could be raised from $18.0^{\circ} \mathrm{C}$ to its boiling point and then evaporated by this energy, assuming sap has the same thermal characteristics as water?

Ze-Han Lee

Numerade Educator

Problem 61

Integrated Concepts
What current must be produced by a 12.0-V battery-operated bottle warmer in order to heat 75.0 g of glass, 250 g of baby formula, and $3.00 \times 10^{2}$ g of aluminum from $20.0^{\circ} \mathrm{C}$ to
$90.0^{\circ} \mathrm{C}$ in 5.00 $\mathrm{min}$ ?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 62

Integrated Concepts
How much time is needed for a surgical cauterizer to raise the temperature of 1.00 g of tissue from $37.0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ and then boil away 0.500 $\mathrm{g}$ of water, if it puts out 2.00 $\mathrm{mA}$ at 15.0 $\mathrm{kV} ?$ lgnore heat transfer to the surroundings.

Ze-Han Lee

Numerade Educator

Problem 63

Integrated Concepts
Hydroelectric generators (see Figure 20.46$)$ at Hoover Dam produce a maximum current of $8.00 \times 10^{3}$ A at 250 $\mathrm{kV}$ . (a) What is the power output? (b) The water that powers the
generators enters and leaves the system at low speed (thus its kinetic energy does not change) but loses 160 m in altitude. How many cubic meters per second are needed, assuming 85.0% efficiency?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 64

64. Integrated Concepts
(a) Assuming 95.0$\%$ efficiency for the conversion of electrical power by the motor, what current must the $12.0-\mathrm{V}$ batteries of a 750 -kg electric car be able to supply: (a) To accelerate from rest to 25.0 $\mathrm{m} / \mathrm{s}$ in 1.00 $\mathrm{min}$ (b) To climb a $2.00 \times 10^{2}-\mathrm{m}$-high hill in 2.00 $\mathrm{min}$ at a constant $25.0-\mathrm{m} / \mathrm{s}$ speed while exerting $5.00 \times 10^{2} \mathrm{N}$ of force to overcome air resistance and friction? (c) To travel at a constant $25.0-\mathrm{m} / \mathrm{s}$ speed, exerting a $5.00 \times 10^{2} \mathrm{N}$ force to overcome air resistance and friction? See Figure 20.47.

Ze-Han Lee

Numerade Educator

Problem 65

Integrated Concepts
A light-rail commuter train draws 630 A of 650-V DC electricity when accelerating. (a) What is its power
consumption rate in kilowatts? (b) How long does it take to reach 20.0 m/s starting from rest if its loaded mass is $5.30 \times 10^{4} \mathrm{kg},$ assuming 95.0$\%$ efficiency and constant power? (c) Find its average acceleration. (d) Discuss how the acceleration you found for the light-rail train compares to what might be typical for an automobile.

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 66

Integrated Concepts
(a) An aluminum power transmission line has a resistance of 0.0580$\Omega / \mathrm{km}$ . 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.

Ren Jie Tuieng

Numerade Educator

Problem 67

Integrated Concepts
(a) An immersion heater utilizing 120 $\mathrm{V}$ can raise the temperature of a $1.00 \times 10^{2}-\mathrm{g}$ aluminum cup containing 350 g of water from $20.0^{\circ} \mathrm{C}$ to $95.0^{\circ} \mathrm{C}$ in 2.00 min. Find its resistance, assuming it is constant during the process. (b) A
lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 68

Integrated Concepts
(a) What is the cost of heating a hot tub containing 1500 $\mathrm{kg}$ of water from $10.0^{\circ} \mathrm{C}$ to $40.0^{\circ} \mathrm{C}$ , assuming 75.0$\%$ efficiency to account for heat transfer to the surroundings? The cost of electricity is 9 cents/kW ? h . (b) What current was used by the 220-V AC electric heater, if this took 4.00 h?

Ze-Han Lee

Numerade Educator

Problem 69

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

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 70

Unreasonable Results
(a) What current is needed to transmit $1.00 \times 10^{2}$ MW of power at 10.0 $\mathrm{kV} ?$ (b) Find the resistance of 1.00 $\mathrm{km}$ of wire that would cause a 0.0100$\%$ power loss. (c) What is the diameter of a 1.00-km-long copper wire having this resistance? (d) What is unreasonable about these results? (e) Which assumptions are unreasonable, or which premises are inconsistent?

Ren Jie Tuieng

Numerade Educator

Problem 71

Construct Your Own Problem
Consider an electric immersion heater used to heat a cup of water to make tea. Construct a problem in which you calculate the needed resistance of the heater so that it increases the temperature of the water and cup in a reasonable amount of time. Also calculate the cost of the electrical energy used in your process. Among the things to be considered are the voltage used, the masses and heat
capacities involved, heat losses, and the time over which the heating takes place. Your instructor may wish for you to consider a thermal safety switch (perhaps bimetallic) that will halt the process before damaging temperatures are reached in the immersion unit.

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 72

(a) What is the hot resistance of a $25-\mathrm{W}$ light bulb that runs on $120-\mathrm{V} \mathrm{AC}$ ? (b) If the bulb's operating temperature is $2700^{\circ} \mathrm{C},$ what is its resistance at $2600^{\circ} \mathrm{C} ?$

Ren Jie Tuieng

Numerade Educator

Problem 73

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

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 74

A certain circuit breaker trips when the rms current is 15.0 A. What is the corresponding peak current?

Ze-Han Lee

Numerade Educator

Problem 75

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?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 76

A North American tourist takes his 25.0-W, 120-V AC razor to Europe, finds a special adapter, and plugs it into 240 V AC. Assuming constant resistance, what power does the razor consume as it is ruined?

Ze-Han Lee

Numerade Educator

Problem 77

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 $\mathrm{kV}$ ? (b) Find the power loss in a $1.00-\Omega$ transmission line. (c) What percent loss does this represent?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 78

A small office-building air conditioner operates on 408-V AC and consumes 50.0 kW. (a) What is its effective resistance? (b) What is the cost of running the air conditioner during a hot summer month when it is on 8.00 h per day for 30 days and electricity costs 9.00 cents/kW ? h ?

Ze-Han Lee

Numerade Educator

Problem 79

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

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 80

What is the peak current through a 500-W room heater that operates on 120-V AC power?

Ze-Han Lee

Numerade Educator

Problem 81

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?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 82

Nichrome wire is used in some radiative heaters. (a) Find the resistance needed if the average power output is to be 1.00 kW utilizing 120-V AC. (b) What length of Nichrome wire, having a cross-sectional area of 5.00 $\mathrm{mm}^{2}$ , is needed if the operating temperature is $500^{\circ} \mathrm{C} ?(\mathrm{c})$ What power will it draw when first switched on?

Ze-Han Lee

Numerade Educator

Problem 83

Find the time after $t=0$ when the instantaneous voltage of $60-\mathrm{Hz}$ AC first reaches the following values: (a) $V_{0} / 2$ (b) $V_{0}(\mathrm{c}) 0$

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 84

(a) At what two times in the first period following $t=0$ does the instantaneous voltage in $60-\mathrm{Hz}$ AC equal $V_{\mathrm{rms}} ?$ (b) $-V_{\mathrm{rms}} ?$

Ze-Han Lee

Numerade Educator

Problem 85

(a) How much power is dissipated in a short circuit of 240 -V AC through a resistance of 0.250$\Omega$ ? (b) What current flows?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 86

What voltage is involved in a $1.44-\mathrm{kW}$ short circuit through a $0.100-\Omega$ resistance?

Ze-Han Lee

Numerade Educator

Problem 87

Find the current through a person and identify the likely effect on her if she touches a $120-\mathrm{VAC}$ source: (a) if she is standing on a rubber mat and offers a total resistance of 300 $\mathrm{k} \Omega$ i (b) if she is standing barefoot on wet grass and has a resistance of only 4000 $\mathrm{k} \Omega$ .

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 88

While taking a bath, a person touches the metal case of a radio. The path through the person to the drainpipe and ground has a resistance of 4000$\Omega$ . What is the smallest voltage on the case of the radio that could cause ventricular fibrillation?

Ze-Han Lee

Numerade Educator

Problem 89

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?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 90

(a) During surgery, a current as small as 20.0$\mu \mathrm{A}$ applied directly to the heart may cause ventricular fibrillation. If the resistance of the exposed heart is 300$\Omega$ , what is the smallest voltage that poses this danger? (b) Does your answer imply that special electrical safety precautions are needed?

Ze-Han Lee

Numerade Educator

Problem 91

(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?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 92

A heart defibrillator passes 10.0 A through a patient's torso for 5.00 ms in an attempt to restore normal beating. (a) How much charge passed? (b) What voltage was applied if 500 J of energy was dissipated? (c) What was the path's resistance? (d) Find the temperature increase caused in the 8.00 kg of affected tissue.

Ze-Han Lee

Numerade Educator

Problem 93

Integrated Concepts
A short circuit in a 120 -V appliance cord has a $0.500-\Omega$ resistance. Calculate the temperature rise of the 2.00 g of surrounding materials, assuming their specific heat capacity is 0.200 $\mathrm{cal} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ and that it takes 0.0500 s for a circuit breaker to interrupt the current. Is this likely to be damaging?

Manish Haldankar

Manish Haldankar

Numerade Educator

Problem 94

Construct Your Own Problem
Consider a person working in an environment where electric currents might pass through her body. Construct a problem in which you calculate the resistance of insulation needed to protect the person from harm. Among the things to be considered are the voltage to which the person might be exposed, likely body resistance (dry, wet, ...), and acceptable currents (safe but sensed, safe and unfelt, ...).

Ren Jie Tuieng

Numerade Educator

Problem 95

Integrated Concepts
Use the ECG in Figure 20.37 to determine the heart rate in beats per minute assuming a constant time between beats.

Ren Jie Tuieng

Numerade Educator

Problem 96

Integrated Concepts
(a) Referring to Figure 20.37, find the time systolic pressure lags behind the middle of the QRS complex. (b) Discuss the reasons for the time lag.

Ren Jie Tuieng

Numerade Educator