# Electric Power

## Electric Power

Electric power is the rate at which work is done or energy is transformed in an electrical circuit. It is a measure of how much energy is used in a span on time.

When a current “I” flows through a conductor for a time t, work done W is given by:

W = VIt

Where,

V = Potential difference across the two ends of the conductor.

Since, Power is defined as the rate of doing work.

$$Power(P)\,\,=\,\,\frac{Work\,\,Done\,\,(W)}{time(t)}\,\,=\,\,\frac{VIt}{t}\,\,=\,\,VI$$,

Power (P) = VI.

Thus, Electric Power is the product of Electric current and the Potential difference due to which the current flows.

Units of Electric Power:

Power is measured in “Watt”.

1 Watt = 1 Volt x 1 amp

Power of an electric circuit is said to be 1 Watt, if a current of 1 amp flows through it when there is a potential difference of 1 Volt across its ends.

We can measure power in “Kilowatt” also commonly used.

1 Kilowatt = 1000 Watt.

Voltage, Current and Resistance are related by the following relation:

We know that:

V = IR

Where,

R = Resistance of the Circuit.

Therefore, the Electric Power can also be calculated using the following relations:

Power (P) = I² R … (1)

Power (P) = V²/R … (2)

Since, power is the rate of energy consumption, Energy can directly be calculated using:

Power (P) = Et.

Where,

E = Energy consumption.

How to find the Electric Power?

Problem: A 10 V battery is connected to a resistor having resistance of 10Ω. What is the current and power across the resistor?

Solution:

Given,

Voltage (V) = 10V

Resistance (R) = 10Ω

We know that:

$$Current(I)\,\,=\,\,\frac{Voltage(V)}{\operatorname{Re}sis\tan ce(R)}\,\,=\,\,\frac{10V}{10\Omega }\,\,=\,\,1A$$,

Now,

Power (P) = Voltage (V) x Current (I)

= 10 Volts x 1A

= 10 Watts

∴ Power (P) = 10Watts.