Topic  8

Why do we need to know the power of electrical appliances?

Power of an Appliance

The power of an appliance is how much energy it transforms every second.  For example an electric drill converts 500 joules every second into kinetic energy.

The units for power are watts (W) or kilowatts (kW) where:

1 W = 1 J/s

1 kW = 1000 W

The equation for electrical power is:

In triangle form:

Worked Example

Question 1  A lorry starter motor runs off a 24 V DC battery.  Under load it takes a current of 500 A.  What power does it develop as it turns the lorry's engine?  ANSWER

This starter motor can start a petrol engine between 9 and 26 litres (pretty big).

Question 2.  Its power is 7.76 kW.  What current does it take from a 12 V battery to turn the engine?  ANSWER

Question 3.  In fact the starter motor in Question 2 takes a current of 1650 A.  What is the power taken from the battery.  What happens to the power?  What is the efficiency of the motor?  ANSWER

You can see from the result of the last calculation that the starter motor will soon get hot if the engine does not start.  Components that take heavy currents need thick and heavy wires to take the current to them.  They also need to be very heavily built.  This one has a mass of 29 kg.

Heating elements are resistors.  In this case electrical energy is converted straight to heat.

Choosing the Right Fuse for an Appliance

Domestic appliances are connected to the mains by means of a fused plug, which we saw last topic.  Remember that a fuse is a weak link that melts when the appliance takes too big a current.  The BS1362 fuses are available in the following sizes;

• 1 A

• 2 A

• 3 A - common

• 5 A - common

• 7 A

• 10 A - common

• 13 A - very common

Plugs are mostly supplied with a 13 A fuse, and most people don't bother replacing the fuse with one of the correct value.  This can be dangerous for the following reason.  Suppose we have an appliance that takes 250 W from the mains.  Its current would be 1.1 A (how?).  Suppose it developed a fault that made it take 750 W.  Its current would now be 3.3 A.  There would be 500 W being used to heat the appliance up.

Question 4  What do you think would happen to the appliance?  ANSWER

Question 5  If there were a 13 A fuse, would it blow?  ANSWER

Question 6  If there were a 3 A fuse, would it blow?  ANSWER

The result of using a 13 A fuse to protect a 1.1 A appliance could be disastrous.

There are three steps in working out the fuse value for an appliance:

1. Calculate the current from the power.  Current = power ÷ 230 V

2. Look at the fuse values in the BS1362 series.

3. Choose the next highest value above your current.

Worked example

If your current worked out to be 5 A, you wouldn't choose the 5 A fuse, as it would keep blowing.  You would choose the 7 A fuse.

Question 7.  A fan heater is rated at 2000 W.  Which is the best fuse to use in its plug?  ANSWER

Charge and Current

In the last topic we saw that in a current of 1 amp, 6 × 10¹⁸ electrons flowed every second.  We called a packet of 6 × 10¹⁸ electrons a coulomb.  Therefore a current of 1 amp is a flow of charge of 1 coulomb every second.

1 A = 1 C/s

Therefore we can write an equation:

In triangle form:

Worked Example

Question 8  A current of 2.5 A is flowing.  How long does it take for 20 C to flow?  ANSWER

Question 9  It takes 12 s for 108 C to flow.  What is the current?  ANSWER

Why do we want to know the charge?  If we know the charge and the voltage, we can work out the energy transformed.

Energy (J) = power (W) × time (s)

Power (W) = voltage (V) × current (A)

So it doesn't need a genius to see that:

Energy (J) = voltage (V) × current (A) × time (s)

When we charge up batteries, we want to know the charge that they hold.

Energy and Charge

When charge passes through a load (e.g. a resistor) it gives off energy that can be used to do a useful job of work (e.g. heat up some water).  If 1 coulomb of charge goes through a resistor which has a p.d. of 1 volt across it, it gives of 1 joule of energy.

We can write this as an equation:

In triangle form:

Above we saw that:

Energy (J) = voltage (V) × current (A) × time (s)

Now

Charge = current × time

So it doesn't take a genius to see that:

Energy = voltage × charge.

Worked Example

Question 10  20000 J of energy is transformed by a 230 V light bulb.  How much charge is this?  ANSWER

Now answer Question 11

Have a go at the Crossword that gets you to think about mains electricity.

Now try the Topic Quiz

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