# What is Electrical Power? Definition, Formulas, Units And Dimensions

All of us know how electricity plays a very important role in our day-to-day lives. In this world of electricity, all is a play of electrical energy. This electrical energy causes electrical power. Whenever this electrical energy flows (or electric current flows) it does some work. The rate at which work is done due to this electrical energy is known as electrical power.

So in today's lesson, we are going to explore this electrical power, how it is defined in physics, its mathematical expression, units, and dimensions.

# What is Electrical Power?

We generally know that power is the rate at which work is done. When this work is done in an electrical circuit with respect to time, it is called electrical power.

This electrical power depends on two main factors. These factors are:

1. The electric current (I) passes through the electrical circuit.
2. The potential difference/voltage (V) across the two ends of the electrical circuit.

Actually, if a source of voltage V sends a current I through a circuit for time t, then the electrical work done in that circuit is W = VIt.

As we see

$Electrical\;Power\;(P)=\frac{Electrical\;Work\;(W)}{Time\;(t)}$

Therefore electrical power

$P=\frac{VIt}{t}$

$Or\;P=VI$

$i.e\;Electric\;Power=Voltage\;\times Electrical\;Current$

This is the formula to find electrical power in an electric circuit. Now to solve various problems or easily memorize this formula you can use this electrical power triangle shown below.

We can derive another formula for electrical power by using Ohm's law.

As we know from Ohm's law V = IR, where R is the resistance.

Now if we substitute the value of the voltage into the power formula then we get

$P=I\times R\times I$

$Or\;P=I^{2}R$

$i.e\;Power=(Current)^{2}\times Resistance$

## Units of Electrical Power

The SI unit of electric power is Joule per second (J/s) or Watt (W) and the CGS unit of electric power is Erg per second (erg/s).

As we know

$Electrical\;Power\;(P)=\frac{Electrical\;Work\;(W)}{Time\;(t)}$

$\therefore\;1\;Watt=\frac{1\;Joul}{1\;Second}$

1 Watt: 1 watt is the measure of electrical power of an appliance which consumes energy at the rate of 1 joule in 1 second.

Larger units like kilowatts (kW) or megawatts (MW) are often used for more significant power levels.

You must know - 1 kW = 10³ W, 1 MW = 10⁶ W

## Dimensions of Electrical Power

The dimension of electrical work is [ML²T⁻²] and the dimension of time is [T].

As we know

$Electrical\;Power\;(P)=\frac{Electrical\;Work\;(W)}{Time\;(t)}$

Therefore the dimension of electrical power = [ML²T⁻²][T⁻¹] = ML²T⁻³.