Electric Circuits · Grade 10

Why do the lights dim for a moment when a large motor starts?

Because every source has internal resistance. The motor draws a large current as it starts, and that current loses voltage inside the source and in the wiring, so the voltage reaching the rest of the house drops briefly. Once the motor is up to speed the current falls and the voltage recovers.

Learning objectives

The battery is not ideal

The electromotive force is the voltage a source would give if no current passed through it at all. That is the number printed on the battery.

In practice there is resistance inside the battery too, and when current flows some energy is dissipated there. The voltage reaching the external terminals is lower.

The calculation is direct: the terminal voltage is the electromotive force minus the current times the internal resistance. The larger the current, the larger the drop — and that is the whole of the dimming lights.

A short circuit

A short is a path of almost no resistance between the two sides of the source. By Ohm's law, a resistance near zero means an enormous current.

That current produces heat at a tremendous rate — current squared times resistance — so a short burns wiring and starts fires. A shorted battery becomes dangerously hot within seconds.

Internal resistance is also what limits the current in a short. Without it the current would be mathematically infinite; in practice it is what decides how bad things get.

Three guardians, three jobs

A fuse protects the wiring. It is a thin wire that melts when the current rises above its rating, breaking the circuit before the cables get hot enough to ignite anything.

An earth wire protects a person from a metal casing that has become live. It gives the fault current an easy path to earth, and usually blows the fuse on the way.

A residual current device protects a person differently: it compares the current going in with the current coming back, and if some is missing — a sign it has found another route, such as through a body — it disconnects within milliseconds. All three complement each other and none replaces the other two.

Worked examples

  1. A battery of emf 12 V and internal resistance 0.5 ohms supplies 4 A. What is the terminal voltage?

    1. The internal drop is the current times the internal resistance
    2. 4 times 0.5 is 2 V
    3. 12 minus 2

    Answer: 10 volts

  2. The same battery with no load at all. What will a voltmeter read at its terminals?

    1. With no load there is no current
    2. No current means no internal drop

    Answer: 12 volts — the electromotive force itself

  3. What does an RCD protect against that a fuse does not?

    1. A fuse responds to too much current in the circuit
    2. A person touching a live wire may pass a current too small to blow it
    3. An RCD detects the difference between the current going in and coming back

    Answer: Current leaking through a person — too small to blow a fuse and enough to kill

Common mistakes

Assuming a battery's voltage is fixed
It falls as the current grows, because of internal resistance. The number printed on the battery is the no-load value only.
Thinking a fuse protects a person
A fuse protects the wiring from fire. The current that can kill a person is far smaller than the one that blows a fuse, which is why an RCD exists.
Treating the earth wire and the RCD as the same thing
The earth wire gives fault current a path to earth; the RCD notices that less current is returning than left and disconnects. They work differently and complement each other.

What to remember

More in Electric Circuits