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Ohm's law

Electricity and magnetism · level 5, lesson 2 of 6

A question to start

Double the voltage across a resistor. Does the current double too, or does something else happen?

The idea

For a metal wire or a resistor kept at the same temperature, the current is proportional to the voltage. Double the voltage and the current doubles. This is Ohm's law:

\[V = IR,\]

with \(R\) staying the same. A part that obeys it is called ohmic. Its graph of current against voltage is a straight line through the origin, and a steeper line means a smaller resistance.

A bulb is not ohmic. As the current grows, its filament heats up, its resistance rises, and the graph curves over.

resistor: straightbulb: curvesvoltagecurrent

Worked examples

1. Find the current. 9 V across 180 \(\Omega\): \(I = 9/180 = 0.05\) A.

2. Find the voltage. 0.2 A through 60 \(\Omega\): \(V = 0.2 \times 60 = 12\) V.

3. Double it. 9 V gave 0.05 A, so 18 V gives 0.10 A: the same \(R = 180\ \Omega\).

Try it

  1. Find the current when 24 V is across 8 \(\Omega\).
  2. What voltage drives 1.5 A through 4 \(\Omega\)?
  3. A resistor carries 0.3 A at 6 V. What current at 15 V?
  4. Why is a bulb's graph of current against voltage not a straight line?
Answers
  1. \(24/8 = 3\) A.
  2. \(1.5 \times 4 = 6\) V.
  3. \(R = 20\ \Omega\), so \(15/20 = 0.75\) A.
  4. Its filament gets hotter as the current rises, so its resistance rises.

Common mistake

"\(V = IR\) is true for everything." \(R = V/I\) always defines resistance. But only an ohmic part keeps the same \(R\) as the voltage changes.

Where it leads