# Electrical Power

## Electrical Power

The power of any device, electrical or mechanical, is a measure of the energy transferred by the device per second. The more ‘powerful’ a device is the more energy it transfers in a given amount of time.

All electrical devices have a power rating on them by law. This might be in the form of the actual power in Watts or by indicating the current and voltage of the device. The higher the rating the more energy it will use and thus the more expensive the device is to use.

A typical laptop will have a power rating of around 50 Watts, meaning it draws in 50 joules of energy from the battery or mains every second. An electric cook has a power rating of 3,500 Watts. The cooker is using 70 times as much electricity as the laptop and is 70 times more expensive to use.

Power in physics is the energy transferred per second and can be represented by the equation:

Power = Energy time or *P = E __÷__ t*

In an electrical circuit the energy can be calculated from *E =ItV*

So *P= ItV __÷__ t _ _giving P =IV* _ Electrical Power =Current x Voltage_

## Calculating Electrical Power

*P =IV Electrical Power = Current x Voltage*

The amount of energy transferred per second by an electrical device is the product of its current and voltage. This is because the voltage provides the energy that is carried by the electrons that form the current, so the higher the voltage the higher the energy of the electrons and the greater the number of electrons moving the higher the overall energy being transferred per second.

Worked Example

What is the power rating of a laptop with a 19.5 V supply generating a current of 2.31 A?

*P = IV = 2.31 A x 19.5 V = 45.05 Watts*

What is the current flowing in a 60 W bulb connected to the mains?

UK mains voltage = 230 V

*P = IV so I = P V = 60 _÷* 230 = 0.26 A_

Although the power of a device can be calculated from just the voltage and the current it is possible to calculate it from knowing the current and the resistance of the device.

*If P = IV and from Ohm’s Law V = IR then P = I x IR = I*^{2}*R*

*Giving Power = Current*^{2}_ x Resistance P = I_^{2}*R*

Example

A current of 2 A flows through a 4 resistor, what is the power rating of the circuit?

*P =I*^{2}*R = 2*^{2}_ x 4 =16 Watts_

- A 20 Ω speaker is supplied by a 1.5A supply, calculate the power rating of the speaker.
- Your answer should include: 45W / 45

Explanation:*P = I²R = 1.5² x 20 = 45 Watts* - A 100 W bulb is connected to the UK mains, calculate the resistance and current for the bulb.
- 540.8

Explanation:*UK mains voltage = 230 V P = IV so I = P V = 100 230 = 0.43 A P =I²R so R = P I² = 100 (0.43)² = 540.8 Ω*