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Electrical Power

Current carries electrical energy to a light bulb, a fan or an electric kettle.

We are interested in the power of the appliance. In a light bulb, this means how much electrical energy is converted to light every second. In an electric kettle, power is the amount of electrical energy converted to heat per second. In a fan, the power is the electical energy converted to mechanical energy per second.

This is important because, at home, we pay for the amount of electrical energy that we use each month. For example, if we use a light bulb that has lower power rating, then we save some money on the electricity bill

Electrical power of an appliance is given by the formula

power = voltage × current,

where voltage is the potential difference across the appliance (e.g. light bulb) and current is the current that flows through it.

To understand why, think of the light bulb. Remember that potential difference is the amount of work done to move 1 C of charge through the light bulb. This work is converted into light and some heat energy. To find the power, we use the formula

power = energy / time,

where energy is equal to work done on the charge.

To relate this to potential difference, suppose that an amount of charge is moved through the light bulb during a certain time. Recall that

voltage = work done / charge.

Since work done is converted to energy, lets write this as

voltage = energy / charge.

Make energy the subject of the formula - multiply both sides by charge:

voltage x charge = energy.

Then the power can be written as

power = energy / time = voltage x charge / time.

But charge / time = current. So

power = voltage x current,

which is the formula for power. So this is the explanation.

Another useful formula is

energy = voltage x current x time.

This comes from

energy = power x time = voltage x current x time.

The two main formulae are often written in these forms:

P = VI and E = VIt,

where P is power, E is energy, V is voltage, I is current and t is time.

Exercise. A light bulb is connected to a 240 V supply. The current that flows through it is 0.1 A. What is the rate at which light and heat is emitted by the light bulb?

Answer. Light and heat are the energy that is converted from electrical energy. The rate at which they are emitted is just the power. To find this, use P = VI = 240 x 0.1 = 24 W.

Exercise. A light bulb is connected to a 240 V supply for 10 seconds. The current that flows through it is 0.1 A. How much light and heat energy is emitted by the light bulb?

Answer. The energy converted from electrical energy is given by E = VIt. So E = 240 x 0.1 x 10 = 240 J.

Exercise. The power rating of a light bulb is 24 W, 240 V. Find the resistance of the light bulb.

Answer. This means that if 240 V is applied to the light bulb, the power of light and heat given out is 24 W. We can find the resistance R using Ohm's law V = IR if we know the current I. We can find I using P = VI.

Divide both sides by V to give P/V = I. So I = P/V = 24/240 = 0.1 A. Then divide both sides of Ohm's law by I to give V/I = R. So the resistance R = V/I = 240/0.1 = 2400 Ω.