# Lesson 6: Electrical Power

## Introduction

In this lesson we'll look at the difference between power and energy. We'll see how to calculate electrical power and how to understand power ratings you see marked on electrical devices.

## Basic idea of power

Power tells us how quickly energy is converted.

Some bulbs are designed to be brighter than other bulbs even if they run from the same type of battery. The brighter bulb will be more powerful because it converts electrical energy to light energy quicker than the dimmer one.

## How our animations show electrical power

In our animations, power is shown by the speed of the expanding red energy circle around the bulb. The quicker the circle moves the higher the power we are showing.

You can use the animations to see that when three bulbs are connected across the same voltage the most powerful bulb will be brightest and have the biggest current flowing throught it. When charges move quickly then energy must be being transferred to the bulb quickly.

## Simple calculation of power

The unit of power is the watt, named in of the inventor of the steam engine, the 18th century Scotsman, James Watt.

1 watt means you transfer energy at a rate of 1 joule per second. 2 watts means you transfer energy at a rate of 2 joules per second and so on.

## Why power depends on both current and voltage

It should make sense that energy is transferred quickly (power is high) if lots of charges arrive at a component each second (i.e. big current) and each charge transfers lots of energy (i.e. big p.d.).

Energy is transferred slowly (power is low) if only a few charges arrive each second (i.e. small current) and each charge transfers only a small amount of energy (i.e. small p.d.).

This is why power depends on both current and voltage.

## Using P = I V

The special formula for electrical power is

power = current x voltage

For example if a lamp with 2 A flowing through it and a p.d. of 6 V across it will have a power of 12 W.

## Power ratings of electrical equipment

If you look on a lightbulb you may see something like 240 V, 100 W. This doesn't mean that the bulb will always have 240 V across it or that it will always convert energy at a rate of 100 W.

What it means is 'If you happen to connect 240 V across this bulb then it will convert energy at a rate of 100 W.'

If you connect it across a lower voltage then its power will be less than 100 W and it'll be dimmer. If you connect it across a higher voltage then its power will be more than 100 W and it'll be brighter.

If you connect it across much more than 240 V then the bulb filament will probably burn out and the bulb won't work. So 240 V is called the operating voltage. It's the voltage that the bulb is designed to work at.

## Changing the number of batteries, changing the number of bulbs

It's a common error to think that if you double the number of batteries then you roughly double the brightness of a bulb. A similar mistake is to think that two bulbs in series are about half as bright as one bulb alone.

The key point to remember is that brightness depends on both current AND voltage.

If you double the number of batteries then you double the voltage and so you also roughly (because the resistance of a bulb changes with current) double the current. This means that doubling the number of batteries roughly quadruples the brightness.

Similarly if you have two bulbs in series they are each about a quarter as bright as a single bulb. This is because roughly doubling the resistance roughly halves the current through each bulb but each bulb also only gets half the voltage.

## P = I^{2}R and P = V^{2}/R

You can combine P = IV with V = IR to give two useful equations.

If we eliminate V we end up with P = I^{2}R.

This means if you double the current then you quadruple the power. At first glance this equation may seem to suggest that if you keep the current constant then increasing the resistance increases the power. But if you increase the resistance you can only keep the current constant by increasing the voltage so it's never really a fair comparison.

Low resistance bulbs are generally brighter than high resistance bulbs if they're connected across the same voltage because the current through them is bigger.

If we eliminate I we end up with P = V^{2}/R.

This means if you double the voltage you quadruple the power. This makes more sense because doubling voltage also doubles current (roughly). The equation also says that if you keep voltage constant and decrease the resistance then you increase the power. This is because if you decrease resistance you increase the current and so increase the power.