Skip to content

Resistance

Electricity and magnetism · level 5, lesson 1 of 6

A question to start

Put the same 6 V across a short thick copper wire, a bulb and a long thin pencil lead. The currents are wildly different. What decides how much current flows?

The idea

Resistance measures how hard a part makes it for current to flow through it. It is defined as

\[R = \frac{V}{I},\]

the voltage across the part divided by the current through it. Resistance is measured in ohms (\(\Omega\)): a part has 1 \(\Omega\) if 1 V drives 1 A through it.

Resistance is bigger for:

  • a longer wire;
  • a thinner wire;
  • a material that conducts less well (nichrome more than copper);
  • most metals, a hotter wire.

A resistor is a part made to have a set resistance, used to control the current in a circuit.

current IRvoltage V across it

Worked examples

1. A resistor. 6 V drives 0.03 A: \(R = 6/0.03 = 200\ \Omega\).

2. A bulb. 3 V drives 0.25 A: \(R = 3/0.25 = 12\ \Omega\).

3. A thick wire. 0.1 V drives 2 A through a short copper wire: \(R = 0.1/2 = 0.05\ \Omega\), very small.

Try it

  1. 12 V drives 0.5 A through a heater element. Find its resistance.
  2. Which has more resistance: a long thin wire or a short thick one, of the same metal?
  3. A part has 1,000 \(\Omega\). What current does 5 V drive through it?
  4. What is a resistor for?
Answers
  1. \(12/0.5 = 24\ \Omega\).
  2. The long thin wire.
  3. \(I = V/R = 5/1000 = 0.005\) A, 5 mA.
  4. To set or limit the current in a circuit.

Common mistake

"Resistance uses up current." The current is the same going in and coming out. Resistance sets how big that current is for a given voltage, and the part turns electrical energy into heat or light.

Where it leads