  # Electric Current, Resistance, and Ohm's Law

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This pack examines current, Ohm's law, resistance and resistivity, power and energy, alternating vs direct currents, and more.

PE 20.1

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? (answer in mA)

PE 20.2

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

PE 20.3

What is the current when a typical static charge of 0.250 µC moves from your finger to a metal doorknob in 1.00 µs ? (answer in A)

PE 20.4

Find the current when 2.00 nC jumps between your comb and hair over a 0.500 - µs time interval. (answer in mA)

PE 20.5

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

PE 20.6

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

PE 20.8

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

PE 20.11

The batteries of a submerged non-nucleaR$_{s}$ ubmarine supply 1000 A at full speed ahead. How long does it take to move Avogadro's number (6.02×10$^{23}$ ) of electrons at this rate? (answer in s)

PE 20.14

Repeat the above example on Example 20.3, but for a wire made of silver and given there is one free electron peR$_{s}$ ilver atom. (answer in ×10$^{-4}$ m/s)

PE 20.15

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. (answer in ×10$^{-4}$ m/s)

PE 20.16

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.) (answer in A)

PE 20.17

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.) How many electrons are in the beam? (answer in ×10$^{13}$ electrons)

Figure: Electrons circulating in the storage ring called SPEAR constitute a 20.0-A current. Because they travel close to the speed of light, each electron completes many orbits in each second PE 20.18

What current flows through the bulb of a 3.00-V flashlight when its hot resistance is 3.60 ? ? (answer in A)

PE 20.19

Calculate the effective resistance of a pocket calculator that has a 1.35-V battery and through which 0.200 mA flows. (answer in k?)

PE 20.20

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? (answer in ×10$^{-2}$ Ω?)

PE 20.21

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? (answer in V)

PE 20.23

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

PE 20.24

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

PE 20.25

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. (answer in Ω)

PE 20.26

If the 0.100-mm diameter tungsten filament in a light bulb is to have a resistance of 0.200 Ω at 20.0ºC, how long should it be? (answer in ×10$^{-2}$ m)

PE 20.27

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).

PE 20.28

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 in ×10$^{-3}$ A)

PE 20.32

An electronic device designed to operate at any temperature in the range from -10.0ºC to 55.0ºC contains pure carbon resistors. By what factor does their resistance increase over this range?

PE 20.36

A copper wire has a resistance of 0.500 Ω at 20.0ºC, and an iron wire has a resistance of 0.525 Ω at the same temperature. At what temperature are their resistances equal? (answer in ºC)

PE 20.40

What is the power of a 1.00×10$^{2}$ MV lightning bolt having a current of 2.00 × 10$^{4}$ A ? (answer in ×10$^{12}$ W)

PE 20.41

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? (answer in kW)

PE 20.42 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.) (answer in ×10$^{-4}$ W)

Figure: The strip of solar cells just above the keys of this calculator convert light to electricity to supply its energy needs. (credit: Evan-Amos, Wikimedia Commons)

PE 20.43

How many watts does a flashlight that has 6.00×10$^{2}$ C pass through it in 0.500 h use if its voltage is 3.00 V? (answer in W)

PE 20.49

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

PE 20.50 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. (answer in \$/y) Figure: On-demand electric hot water heater. Heat is supplied to water only when needed. (credit: aviddavid, Flickr)

PE 20.51

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? (answer in cents)

PE 20.54

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? (answer in h)

PE 20.56

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 . (answer in billion dollars /year)

PE 20.58

00-gauge copper wire has a diameter of 9.266 mm. Calculate the power loss in a kilometer of such wire when it carries 1.00×10$^{2}$ A . (answer in W)

PE 20.61

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 3.00×10$^{2}$ g of aluminum from 20.0ºC to 90.0ºC in 5.00 min? (answer in A)

PE 20.62

Integrated concepts

How much time is needed for a surgical cauterizer to raise the temperature of 1.00 g of tissue from 37.0ºC to 100ºC 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 in s)

PE 20.73

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

PE 20.74

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

PE 20.75

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? (answer in ms)

PE 20.79

What is the peak power consumption of a 120-V AC microwave oven that draws 10.0 A? (answer in kW)

PE 20.80

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

PE 20.86

What voltage is involved in a 1.44-kW short circuit through a 0.100 - ? resistance? (answer in V)

PE 20.89

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? (answer in ×10$^{5}$ ?)

PE 20.95

Integrated concepts Use the ECG in Figure to determine the heart rate in beats per minute assuming a constant time between beats. (answer in beats/min)

Figure: A lead II ECG with corresponding arterial blood pressure. The QRS complex is created by the depolarization and contraction of the ventricles and is followed shortly by the maximum oR$_{s}$ ystolic blood pressure. See text for further description. CC BY - OpenStax