Electromagnetic Induction and Household Circuits: Quick Revision

A brief note on Electromagnetic Induction and Household Circuits. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• A current is induced in a coil while the field through it changes: when a magnet and the coil move relative to each other.
• It is larger for faster motion, a stronger magnet and more turns. It reverses when the motion reverses, and it opposes the change (Lenz's law).
• Fleming's right-hand rule: thumb for the motion, forefinger for the field, middle finger for the induced current.
• A generator turns a coil in a field. Slip rings give AC; a split ring gives a pulsing DC.
• A house has a live, a neutral and an earth wire. Appliances are in parallel. A fuse in the live wire melts when the current is too large; the earth wire protects us from a live metal body.

The facts at a glance

A worked example

A generator's coil turns $2700$ times a minute. Find the frequency, the time of one cycle and the changes of direction each second. Then decide whether a $3000\ \text{W}$ geyser on $220\ \text{V}$ is safe on a $15\ \text{A}$ circuit.

1. Frequency. $f = \dfrac{2700}{60\ \text{s}} = 45\ \text{Hz}$.
2. One cycle. $T = \dfrac{1}{45\ \text{Hz}} = 0.0222\ \text{s} = 22.2\ \text{ms}$.
3. Changes. $2 \times 45 = 90$ each second.
4. The geyser. $I = \dfrac{3000\ \text{W}}{220\ \text{V}} = 13.6\ \text{A}$, less than $15\ \text{A}$: safe.

Practice with new numbers

A program to try

The program repeats the worked example.

Mistakes to avoid

• Expecting a current from a magnet at rest. Only a change of field induces a current.
• Counting the changes of direction as $f$. There are two in every cycle: $2f$.
• Putting the fuse in the neutral wire. It must be in the live wire.
• Replacing a fuse with a thick wire. It would never melt, and the wires could catch fire.

Check yourself

1. A magnet is pushed into a coil and then held still inside it. What does the galvanometer's needle do?

2. How long is one cycle of a $60\ \text{Hz}$ supply, in milliseconds?

3. Why must the fuse be in the live wire?

4. A room heater draws $2420\ \text{W}$ from the $220\ \text{V}$ mains. Will a $10\ \text{A}$ fuse hold?