Power and Joule's Law

Author: E.E. Kimberly

When a continuous current flows in a resistance, the rate at which electrical energy is converted into heat energy is directly proportional to the resistance and to the square of the current. This law was discovered by Joule and bears his name.

By definition, rate of change of energy is power. Therefore, the power in a resistance is

P = RI²          (2-2)

where

P = electrical power, in watts;
R = resistance, in ohms;
I = current, in amperes.

The abbreviation for watt is w. Since R = V/I,

or

(2-3)

Also

(2-4)

The ampere is defined in terms of the cgs system of units. If a conductor 1 cm in length be caused to move with a velocity of 10⁸ cm per sec in and perpendicular to the lines of flux of a magnetic field having a uniform intensity of 1 gauss, an emf of 1 volt will be generated in the conductor (see section Electromotive Force Produced by Motion). If at the same time a current of 1 ampere be caused to flow in the conductor, the reacting force against which the conductor must be moved will be 1/10 dyne (see Lenz's Law). The electrical power generated in the conductor will be

P = VI = 1*1 = 1 watt

The mechanical power input to the conductor will be

P = FD/t

[2-5]

where

P = mechanical power, in dyne-centimeters per second;
F = force on the conductor, in dynes;
D = distance through which the conductor is moved, in centimeters;
t = time, in seconds.

dyne-cm per sec

By the law of conservation of power, the mechanical power must be equal to the electrical power. Hence,

1 watt = 10⁷ dyne-cm per sec

The most commonly used unit of mechanical power is the horsepower. Since 1 hp = 550 ft-lb per sec, 1 ft = 30.48 cm, and 1 lb = 445,072.3 dynes, it follows that

Also, 1 kilowatt = 1000 watts.