# Electrical Power

The power is defined as the work done per unit time. It is clear that work is required to drive charge around a circuit. In particular, if a charge of dQ flows due to a potential difference of V Volts, the work done is given by

dW = VdQ

The power is then

dW/dt =V dQ/dt or

P = VI(1)

Power is measured in Watts [W] or [J.s-1]. The energy from the work done is released in the form of heat

Using Ohm's law, (V=IR), we can substitute for either I or R, in (1) to give alternative equations for the power.

P = I2R

P=V2/R(2)

## Power Rating for various Appliances in the Home

Electrical appliances used around the home are rated in Watts and electricity is sold by the kilowatt-hour. This is equivalent energy used by a device rated at 1000 W running for 1 hour, or 3.6 x 106 J. This is also the same energy as a Board of Trade Unit (BTU) (Not to be confused with the (British Thermal Unit) b.t.u. which describes the power of heating and cooling systems.)

To give some idea of how much energy electrical items consume the table below lists various electrical appliances and their power ratings.

AppliancePower Rating (W)
Water Heater4000
Electric Cooker, Hob (one ring)2000
Electric Cooker, Oven1500-2500
Microwave Oven600-900
Washing Machine 2750
Vacuum Cleaner800 - 1200
Toaster1200
Electric Kettle1200 - 2200
Hair Dryer 1000
Plasma Television328
LCD Television193
CRT Television146
Fridge110
Incandescent Light Bulb40 - 100
Computer78
Laptop Computer65
PlayStation II30
Energy Efficient Light Bulb15
Wireless Router7
CRT Standby3-11
Charging Mobile Phone3
Solar Powered Calculator0.04

The actual cost of running all this equipment depends on how much a kiloWatt of power costs and how long you use each appliance. However, it is clear that the most power hungry appliances are those used for heating things. What is surprising, is the high power consumption of LCD televisions in comparison to traditional CRTs.

### People Power

It also interesting to compare the amount of power used by electrical appliances with the amount of power it is possible for a person to generate. Even just sitting around, a person radiates energy at a rate of 100 W in the form of heat. It has been suggested that this might also be an untapped resource of power. Harnessing that energy would be very difficult because people tend to move around and live lives. Secondly, convertion of energy would be very inefficient. Therefore, if it were possible, the actually usuable power would be much lower than this figure of 100 W. This type of electrical generation is only going to be useful for powering personal electric devices.

Generating electricity by cycling it would not be difficult for a typical person to generate about 60 W for an hour or two by pedalling. A top-athelete can generate up to 366 ± 5 W[1].

It has been suggested [2], perhaps more as a gimick, that we could use the energy expended by people going to the gym as renewable resource. In this example, the members of the gym generate the power for 13 florescent lights. The \$15,000 cost for installing equipment on the 12 machines far outweighs the saving in electricity generated. The same \$15,000 can buy 153,061 kW hrs or enough energy to run the same lights for 163,695 years. There are just far better methods of generating electricity. We could tap all the wasted energy of dogs wagging their tails. In times of peak demand, you could get a man to run up and down in a hot-dog costume. It is possible, but it is not worth the effort for the power generated.

## References

[1] Jerzy A. Zoladz a1 , Arno C. H. J. Rademaker a1 and Anthony J. Sargeant a1 ,"Human muscle power generating capability during cycling at different pedalling rates", Experimental Physiology, 85: 117-124 Cambridge University Press, (2000).

[2] Wall Street Journal Online. California Fitness