Series and parallel circuits: Rtotal = R₁ + R₂

The idea

This equation gives the total resistance of two resistors connected in series. Rtotal is the total resistance in ohms (Ω), R₁ is the resistance of the first component and R₂ is the resistance of the second component. Because the same current passes through both components in turn, the potential differences add, and so the resistances add. For example, if R₁ = 5 Ω and R₂ = 7 Ω, then Rtotal = 5 Ω + 7 Ω = 12 Ω. The equation extends to more than two series components by adding each resistance in turn. It does not apply to parallel circuits, where the total resistance is less than the smallest individual resistance.

What earns the marks

• Identify Rtotal as the total resistance of the series combination, measured in ohms (Ω).
• Substitute the resistance values of R₁ and R₂ into the equation correctly, including units.
• Add the resistance values to find Rtotal, for example 5 Ω + 7 Ω = 12 Ω.
• Extend the method to three or more series resistors by adding each resistance in turn.
• Recognise that the equation applies only to series circuits, not to parallel circuits.

Common mistakes and how to put them right

• Using Rtotal = R₁ + R₂ for parallel resistors.

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

• Mixing units, such as adding 0.5 kΩ to 200 Ω without converting.

  Put it right by converting all resistances to the same unit, for example 500 Ω + 200 Ω = 700 Ω.

• Omitting units from the final answer.

  Put it right by giving the total resistance in ohms (Ω).

Exam tips

• Write the equation Rtotal = R₁ + R₂ before substituting values to make the method clear.
• Convert all resistance values to the same unit before adding them.
• Check that the total resistance is greater than either individual resistance for a series circuit.