Electric Power

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Discussion

James Prescott Joule (1818-1889) England, verified Ohm's Law and determined that the heat delivered by a conductor is directly proportional to its resistance and to the square of the current through it. On the Caloric Effect of Magneto-Electricity, and on the Mechanical Value of Heat. 1843.

electric power from the definition

P =  W  =  ⎛
⎝		 W   ⎞⎛
⎠⎝		 q ⎞
⎠		  = VI
t q t

power in terms of current

P = VI = (IR)I = I2R

power in terms of voltage

P = VI = V  ⎛
⎝		 V ⎞
⎠		  = V2R
R

summary

P = VI = I2R =  V2
R

consumer affairs

A portion of a residential consumer electric bill. Utility companies sell electric energy by the kilowatt hour; a unit that simplifies calculating operating costs for electrical devices. The energy consumed during this particular billing cycle was quite small (when compared to similar consumers), but the rate charged by this utility was approximately double the US average in the year 2000.

Conventional (copper-based) cables are capable of transmitting power (40 to 600 MW) at high voltages (40 to 345 kV)

Line loss

Ploss = I2loadRline =  ⎛
⎝		 Pload ⎞2
⎠		  Rline
Vline

and loss fraction.

loss fraction =  Ploss  =  PloadRline
Pload V2line

Summary

Problems

practice

  1. Read the following description of the execution of Kenneth Stewart in Virginia on 23 September 1998.
    The electric cycle, 1,825 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 … (Source: Amnesty International).
    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.
    Solutions …
    1. Answer it.
    2. Answer it.
  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 electrical generators that provide current for household use. Read this description from the Auto-Free Times.
    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.
    Now answer these questions …
    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?
    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?
    Solutions …
    1. Answer it.
    2. Answer it.
  3. Write something.
    • Answer it.
  4. Write something completely different.
    • Answer it.

numerical

  1. Verify the power calculations of this scientist from Fermi National Accelerator Laboratory.
    [Physicist Sergei] Nagaitsev's group has created a record-breaking electron beam with a continuous [electron] 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.

    Source: Riesselmann, Kurt. "Ecool Celebrates." FermiNews, 1 March 2002: 8-11.
  2. During fair weather there exists an electric potential difference of about 250 to 500 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

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