Series and parallel circuits: solve problems for circuits which include resistors in series using the concept of equivalent resistance.

The idea

Equivalent resistance is the single resistance that would replace a group of resistors without changing the current drawn from the supply. For resistors in series, the equivalent resistance is the sum of the individual resistances: R_eq = R₁ + R₂ + R₃. Once R_eq is known, the circuit behaves as one resistor, so I = V_supply ÷ R_eq gives the current through every component.

For example: A 12 V supply with 3.0 Ω, 4.0 Ω and 5.0 Ω in series has R_eq = 12 Ω, so I = 12 V ÷ 12 Ω = 1.0 A. The equivalent resistance is always larger than the largest individual resistance in the series group, which is a useful check on the answer.

What earns the marks

• Defines equivalent resistance as the single resistance that replaces a series group while drawing the same current from the supply.
• Calculates R_eq by adding the individual resistances, including correct unit conversion for kilohms and milliohms.
• Uses I = V_supply ÷ R_eq to find the current through the whole series circuit after finding the equivalent resistance.
• Uses the equivalent resistance with V = I × R to find the potential difference across a chosen part of the circuit.
• Recognises that the equivalent resistance of a series group is greater than any single resistance in that group and uses this as a check.
• Solves multi-step problems by finding R_eq first, then the current, then any required potential difference or resistance.

Common mistakes and how to put them right

• Adding the reciprocals of the resistances for a series group.

  Put it right: Add the resistances directly for series; reciprocal addition applies to parallel resistors.

• Dividing the supply potential difference by one resistor instead of by the equivalent resistance.

  Put it right: Use R_eq for the whole series group to find the current.

• Mixing units, such as adding 470 Ω to 1.5 kΩ without converting.

  Put it right: Convert all resistances to ohms before adding.

• Assuming the equivalent resistance is smaller than the smallest resistor.

  Put it right: In series, R_eq is larger than the largest individual resistance.

Exam tips

• State the equivalent resistance before calculating the current so each step of the method is clear.
• Convert all resistances to ohms at the start and keep units with every substituted value.
• Check that R_eq is greater than the largest individual resistance before using it.
• For multi-step questions, label each stage, for example R_eq, then I, then V across one resistor.