Series and parallel circuits: the total resistance of two components is the sum of the resistance of each component.

The idea

In a series circuit the current has only one path, so it passes through each component in turn. Each component resists that current, and the battery must drive the current through every resistance, so the total resistance is the sum of the individual resistances. For example, a 4 Ω resistor and a 6 Ω resistor in series give a total resistance of 4 Ω + 6 Ω = 10 Ω. Adding a component always increases total resistance and reduces the current for a fixed potential difference. This rule applies only to components connected in series, not in parallel. In parallel, the total resistance is less than the smallest individual resistance because there are additional paths for the current.

What earns the marks

• State that in a series circuit the current passes through each component in turn along a single path.
• Explain that each component resists the current, so the total resistance is the sum of the individual resistances.
• Calculate total resistance by adding the resistance values of all components in series, for example 4 Ω + 6 Ω = 10 Ω.
• Recognise that adding a component in series increases total resistance and decreases current for a fixed potential difference.
• Distinguish series from parallel: in parallel the total resistance is less than the smallest individual resistance.

Common mistakes and how to put them right

• Adding resistances for components in parallel.

  Put it right by using the parallel rule, where total resistance is less than the smallest individual resistance.

• Forgetting to include every component in the series loop.

  Put it right by listing all resistances in the single path before adding.

• Assuming total resistance is the average of the resistances.

  Put it right by adding the values, since each component resists the same current in turn.

Exam tips

• Identify whether the circuit is series or parallel before choosing a method for total resistance.
• Show the addition of resistance values clearly, including units, so the method is visible.
• Check that the total resistance is larger than any single series resistance; if not, re-examine the circuit.