6.3 Domestic uses and safety — Practise

Work through these on your own. Some questions ask for a description or an explanation, so write in full sentences and keep the science words exact.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

Express a time of 1.5 minutes in seconds.
A mains kettle takes a current of 8.0 A for 90 s. Calculate the charge that flows through it.
State the frequency and the potential difference of the UK domestic supply, and describe the difference between direct and alternating current.
Describe the job of the live wire, the neutral wire and the earth wire in a mains cable.
Explain why a live wire can be dangerous even when a switch in the mains circuit is open.
Explain why the metal case of a mains appliance is connected to the earth wire.
A mains lamp is switched on. Explain why the current in the live wire equals the current in the neutral wire.
State the potential difference between the live wire and earth in a mains circuit, and state the potential of the earth wire.
A mains appliance has a potential difference of 230 V across it and a current of 0.40 A through it. Calculate its resistance.
Two resistors of 6.0 Ω and 18 Ω are connected in series. Calculate the total resistance.
A current of 4.0 A flows for 3.0 minutes. Calculate the charge that flows.
A mains appliance carries a current of 2.5 A for 4.0 minutes. Say which relationship you will use, then calculate the charge that flows.

Answers and concise solutions

1. 1.5 minutes in seconds

Answer: $1.5\,\text{minutes} = 1.5 \times 60 = 90\,\text{s}$ .

2. Charge that flows through the kettle

Answer: $Q = It = 8.0 \times 90 = 720\,\text{C} = 7.2 \times 10^2\,\text{C}$ . The same charge flows back through the neutral wire.

3. The UK supply and the two kinds of current

The UK domestic supply has a frequency of 50 Hz and a potential difference of about 230 V.
A direct current flows in one direction only, like the current from a battery.
An alternating current keeps changing direction, so the potential difference swaps ends many times each second.

4. The three wires and their jobs

The live wire carries the alternating potential difference from the supply.
The neutral wire completes the circuit and is at, or close to, earth potential.
The earth wire is a safety wire at 0 V. It carries a current only if there is a fault, and it stops the case of an appliance becoming live.

5. Why the live wire is still dangerous

The switch might be in the neutral wire, or between the appliance and the live wire.
The wire that goes back to the supply stays at about 230 V. Touching it lets a current flow through the body to earth.

6. Why the metal case is earthed

If the live wire comes loose and touches the metal case, the case would become live.
The earth wire gives the fault current a low-resistance path to earth, so a large current flows to earth and the case does not stay at 230 V.

7. Why the live and neutral currents are equal

The lamp, the live wire and the neutral wire form a single closed loop.
Charge is not used up by the lamp, so the rate of flow of charge is the same in both wires. Only the energy carried by the charge is transferred.

8. The two potential differences

The potential difference between the live wire and earth is about 230 V.
The earth wire is at 0 V.

9. Resistance of the appliance

Answer: $R = \dfrac{V}{I} = \dfrac{230}{0.40} = 575\,\Omega = 5.8 \times 10^2\,\Omega$ to two significant figures.

10. Total resistance of the series pair

Answer: $R_{total} = R_1 + R_2 = 6.0 + 18 = 24\,\Omega$ .

11. Charge that flows

Answer: Change the time to seconds: $3.0 \times 60 = 180\,\text{s}$ . Then $Q = It = 4.0 \times 180 = 720\,\text{C} = 7.2 \times 10^2\,\text{C}$ .

12. Charge that flows

Answer: Use $Q = It$ , with the time in seconds. $4.0 \times 60 = 240\,\text{s}$ , so $Q = 2.5 \times 240 = 600\,\text{C} = 6.0 \times 10^2\,\text{C}$ .