Question

define electric power with mathematical formula and it is unit define 1 volt of power convert 1KWH into Joule

Answer 1

Energy

 

To understand how energy is converted consider a simple circuit with a 'load' * resistor and a D.C. source.

* this could be a heater element, a motor or indeed any component with resistance

 

 

DC circuit PE drop across a resistor

 

 

Charge loses potential energy(PE) as it moves through the resistor. This electrical PE is transformed mostly into heat energy dissipated in the resistor.

The PE is defined as*:

 

work = charge x potential difference

 

W = QV

 

(Joules) = (Coulombs) x (Volts)

 

 

*for more information on this equation see the definition of the volt

 

 

Since,

 

charge = (current) x (time current flows)

 

Q = It

 

(Coulombs) = (Amps) x (seconds)

 

 

therefore, substituting for Q in the work equation,

 

W = (It)V

 

rearranging,

 

W = VIt

 

 

back to top

 

 

Power

 

By definition, 'power' is the rate of working and is equal to the work done divided by the time taken.

 

equation for power

 

 

substituting for W

the power equation #2

 

cancelling the 't'

 

power equation #3

 

 

(Watts) = (Volts) x (Amps)

 

 

note: 1 Watt is a rate of working of 1 Joule per second.

 

 

 

The equation for power can be modified if we make substitutions using Ohm's Law.

 

 

modified power equation

 

 

substituting in the power equation for V ,

 

modified power equation #2

 

substituting in the power equation for I,

 

modified power equation #3

 

 

back to top

 

 

The Kilowatt-hour (kWh)

 

A kilowatt-hour is a unit of energy.

 

By definition, a kilo-watt hour is the amount of energy consumed when a 'rate of working' (power) of 1 kilowatt is used for 1 hour.

 

conversion of 1 kWh to Joules:

 

1 kWh = 1 kW x 1 h = 1000 W x 3600 s = 3600000 J

 

1 kWh = 3.6 x 106 J