Electric power of an electrical appliance or circuit tells us the rate at which electrical energy is consumed by it per unit time. This is denoted by P and measured using the SI unit of power watt or one joule per second.

For example, a bulb of 100 watts power consumes electrical energy at the rate of 100 joules per second (100 J/s or 100 J s

^{–1}).Watt is an important unit of power since it is used in electrical work. Watt is a small unit of power. Sometimes bigger units of power called kilowatt (kW) and megawatt (MW) are also used.

## Electric Power Definition

Electric power is the rate at which electrical energy is consumed by an electric circuit per unit time. It is a scalar quantity. It is denoted by P and its SI unit is Watt or Joule per second.

## Electric Power Formula

Electric Power formula is written as follows: P = VI

Here, P is the Power, V = Potential Difference in the circuit and I is the electric current.

Other formulas of Electric Power derived using Ohm’s law are as follows:

P = I^{2}R

P = V^{2}/R

Here, R stands for the resistance of the circuit.

## SI Unit of Electric Power – Watt

The SI unit of electric power is

wattwhich is denoted by the symbol W.We can now define the unit of power ‘watt’ as follows : 1 watt is the power of an appliance which does work at the rate of 1 joule per second.

We can also define watt by using the term ‘energy’ as follows : 1 watt is the power of an appliance which consumes energy at the rate of 1 joule per second.

We can write an expression for watt as follows :

1 watt =1 joule/1 secondThe unit of power called ‘watt’ is named after a Scottish inventor, engineer and designer James Watt who became famous for improving the design of steam engine.

## Other Units of Electric Power

Watt is a small unit of power. Sometimes bigger units of power called kilowatt (kW) and megawatt (MW) are also used.

1 kilowatt = 1000 watts

or 1 kW = 1000 W

And 1 megawatt = 1000,000 watts

or 1 MW = 1000,000 W

or 1 MW = 10^{6}W

**Horse Power**: Another unit of power is called ‘horse power’ (h.p.) which is equal to 746 watts. Thus,

1 horse power = 746 watts

Brake Horse Power:These days the powers of engines (of cars, and other vehicles, etc.) are expressed in the unit called ‘brake horse power’ (b.h.p.). Brake horse power is the unit of power equal to one horse power which is used in expressing power available at the shaft of an engine. The more powerful a car is, the quicker it can accelerate or climb a hill, that is, more rapidly it does work.

## Power-Energy Formula

Power is the rate of energy consumption.

Power P = E/t …………………… [1] where, E is the electric energy consumed (in Joules) and t is time duration in seconds.

Again E = Work done to move a charge Q through a electric circuit having Potential Difference of V.

E= W = QV ……… [2]

From 1 and 2,

P = QV/t ………….. [3]

## Derivation of Electric power formula [P=VI]

P=E/t = W/t = QV/t = V (Q/t) = VI

=> P = VI

Here, P is the Power, V = Potential Difference in the circuit and I is the electric current.

## Electric Power Sample Numerical Problem

Example:

An electric bulb consumes 7.2 kJ of electrical energy in 2 minutes. What is the power of the electric bulb ?

**Solution. **

We know that :

Power = Energy consumed/Time taken

Here, Energy consumed = 7.2 kJ = 7.2 × 1000 J = 7200 J

And, Time taken = 2 minutes = 2 × 60 seconds = 120 s

Now, putting these values of ‘energy consumed’ and ‘time taken’ in the above formula, we get :

Power =7200 J/120 s

= 60 J/s

= 60 W

Thus, the power of this electric bulb is 60 watts.