Resistors: The current through an ohmic conductor (at a constant temperature) is directly proportional to the potential difference across the resistor. This means that the resistance remains constant as the current changes.

The idea

For an ohmic conductor kept at constant temperature, current I is directly proportional to potential difference V. This means doubling V doubles I, so the ratio V ÷ I is constant. Since resistance is defined as R = V ÷ I, the resistance remains constant as current changes. The current–potential difference graph is a straight line through the origin, and its gradient equals 1 ÷ R. A fixed resistor at room temperature is a common example. If the temperature changes, for example in a filament lamp, the straight-line relationship breaks down and the component becomes non-ohmic. To use this idea, check that the graph is a straight line through the origin, then calculate R from V ÷ I at any point on the line.

What earns the marks

• Direct proportionality means I ∝ V, so doubling V doubles I when temperature is constant.
• The current–potential difference graph for an ohmic conductor is a straight line through the origin.
• Resistance is constant because R = V ÷ I gives the same value at every point on the line.
• The gradient of the I–V graph is equal to 1 ÷ R, so a steeper line means a smaller resistance.
• The condition 'at constant temperature' is essential; a change in temperature can change resistance and destroy the proportionality.
• A fixed resistor at a steady temperature is a standard example of an ohmic conductor.

Common mistakes and how to put them right

• Saying that current is directly proportional to potential difference for all resistors.

  Put it right: This is only true for ohmic conductors at constant temperature.

• Thinking that resistance changes because current changes in an ohmic conductor.

  Put it right: In an ohmic conductor, R is constant, so V and I change together in proportion.

• Reading the gradient of an I–V graph as resistance.

  Put it right: The gradient is 1 ÷ R, so R = 1 ÷ gradient.

• Ignoring the 'constant temperature' condition.

  Put it right: State that temperature must remain constant for the proportionality to hold.

Exam tips

• Quote the equation R = V ÷ I and use it to justify why constant R follows from direct proportionality.
• When interpreting a graph, check that the line passes through the origin and is straight before calling the component ohmic.
• Use the phrase 'directly proportional' only when the graph is a straight line through the origin.
• If a question asks for the resistance from a graph, choose a clear point on the line and calculate V ÷ I.