The Physics
Hypertextbook
Opus in profectus

# Electric Power

## Problems

### practice

1. Read the following description of the execution of Kenneth Stewart in Virginia on 23 September 1998.

The electric cycle, 1825 volts at approximately 7.5 amps for 30 seconds, then 240 volts at approximately 1.5 amps for 60 seconds… a 5 second pause intervenes, and the cycle is repeated, was designed to render the condemned brain dead within the first few moments. The function of the remainder of the cycle is to stop the body's organs so that a physician can certify that death has occurred….

Amnesty International, 1998

Determine…

1. the total electric energy delivered to Mr. Stewart on the day of his execution.
2. his change in temperature assuming assuming a standard 70 kg mass and a body made entirely of water.
2. Humboldt State University in northern California has a unique laboratory devoted to appropriate technology called the Campus Center for Appropriate Technology (CCAT). One of the many innovations pioneered at CCAT is a project known as "pedal power" — a set of stationary bicycles connected to electric generators that provide current for household use.

Most of the energy used to fuel the CCAT house comes from the Sun, but a battery bank is also charged with 24 V permanent magnet DC generators run by exercise bikes in the basement. The flywheel on each bike is furnished with a groove. Through this groove is a belt that is attached to the generator's central shaft. The average person pedaling 70 rpm spins the shaft creating an electrical current of 4 A…. This allows someone to get a comfortable workout while at the same time charging the batteries.

Auto-Free Times, 2001

1. Determine the power output of person pedaling a stationary bicycle at the CCAT house.
2. How much work does the person do in one minute?
3. Over what total distance have the pedals moved in one minute? (Assume a crank arm length of 18 cm.)
4. How fast are the person's feet moving while generating power at the CCAT house?
5. With what average force does a typical person in the CCAT house push down on the pedals?
3. Which of these apparently similar rechargeable batteries is "better"? Answer this by computing the…
1. charge in…
1. milliamp hours [mAh]
2. coulombs [C]
2. potential energy in…
1. milliwatt hours [mWh]
2. joues [J]

Compile your findings in a table like this one.

Two apparently similar rechargeable batteries
type voltage charge energy
(V) (mAh) (C) (mWh) (J)
NiZn 1.6     2500
NiMH 1.2 2500
4. Write something completely different.

### conceptual

1. Why are large voltages used in electric power transmission lines? Why not use large currents instead?

### numerical

1. The useful life of a battery is stated in ampere-hours. A typical 12 V car battery has a discharge time of 60 Ah. Suppose you left the headlights on when your car was parked and that they drew 3 A of current.
2. How much energy would it consume?
2. During fair weather there exists an electric potential difference of about 400 kV between the positively charged ionosphere and the negatively charged surface of the Earth. This gives rise to a steady flow of electrons from the ground to the ionosphere known as the fair weather current. If the intensity of the fair weather current is on the order of 1 W/km2, determine…
1. the fair weather current density
2. the total fair weather current over the entire surface of the Earth
3. the fair weather current through the top of your head in…
1. ampères
2. electrons per second
3. A diesel-electric locomotive can supply a maximum current of 850 amperes at 700 volts to its traction motors for for half an hour. It does this while pulling a train up an incline at a constant speed of 13.4 m/s. Determine the following quantities for a locomotive operating under these circumstances…
1. the combined power of the motors
2. the effective resistance of the circuit containing the motors
3. the work done by the motors in half an hour
4. the pulling force of the locomotive
5. the distance traveled by the train in half an hour
The current to the motors is reduced to 650 amps at 700 volts for the next hour of operation. The pulling force of the locomotive is reduced to 25,600 newtons and the train continues at a new constant speed on a long stretch of level track. Determine the following quantities for a locomotive operating under these circumstances…
1. the combined power of the motors
2. the effective resistance of the circuit containing the motors
3. the work done by the motors in an hour
4. the new speed of the train
5. the distance traveled by the train in an hour
4. Fermi National Accelerator Laboratory is the premiere high energy physics laboratory in the United States. Typical experiments at Fermilab involve producing beams of subatomic particles, accelerating them to high velocities, and them smashing them into stationary targets or other particle beams. Read the following passage from their newsletter,.

[Physicist Sergei] Nagaitsev's group has created a record-breaking electron beam with a continuous current of 500 milliamps at an energy of 3.5 MeV. To the layperson, these numbers may not seem significant. After all, half an amp is the current flowing through the wire of a typical light bulb. However, the electrons in the beam travel at a much higher energy than those in a wire, leading to a beam power that even amazes the non-experts. "We are holding a world record in DC beam power," Nagaitsev said. "About two megawatts." For comparison, this amount of power is sufficient to operate two thousand kitchen refrigerators simultaneously.

FermiNews, 2002

Verify the claims of the author through the following set of calculations…
1. What kind of typical light bulb would have a half an amp of current running through it? (Assume a North American household voltage of 120 V.)
2. Does the beam described by Nagaitsev actually have a power of about two megawatts? Justify your answer with a calculation.
3. What power does Nagaitsev assume a typical home refrigerator needs to operate? Justify your answer with a calculation.
4. What make and model of household refrigerator would require the approximate power you calculated in part c.?
5. Purchase the refrigerator you identified in part d.