V = IR in series and parallel circuits

Electricity

GCSE Physics (8463)

ORIGINAL

The same two resistors in series, then in parallel: share the p.d., add the branch currents, and explain why parallel resistance falls.

Board and spec code confirmed against AQA 8463 · registry checked 2026-07-17How this checking works

Question

4.0\,\Omega

resistor and an

8.0\,\Omega

resistor are connected in series to a

12\,\text{V}

battery. (a) Calculate the current in the circuit and the potential difference across the

8.0\,\Omega

resistor. (b) The two resistors are then reconnected in parallel across the same battery. Calculate the current from the battery and explain why the total resistance is now less than

4.0\,\Omega

Every step worked, with the reasoning.

1
Series: $R_{\text{total}} = R_1 + R_2 = 4.0 + 8.0 = 12\,\Omega$
In series, the total resistance is the sum of the resistances.
2
$I = \dfrac{V}{R} = \dfrac{12}{12} = 1.0\,\text{A}$
Rearrange $V = IR$ . In series the same current passes through every component.
3
$V_{8.0\,\Omega} = IR = 1.0 \times 8.0 = 8.0\,\text{V}$
Check: $4.0\,\text{V} + 8.0\,\text{V} = 12\,\text{V}$ — in series the battery's potential difference is shared between the components.
4
Parallel: each resistor has the full $12\,\text{V}$ , so $I_{4.0\,\Omega} = \dfrac{12}{4.0} = 3.0\,\text{A}$ and $I_{8.0\,\Omega} = \dfrac{12}{8.0} = 1.5\,\text{A}$
In parallel, the potential difference across each branch is the same as the supply.
5
$I_{\text{battery}} = 3.0 + 1.5 = 4.5\,\text{A}$ , so $R_{\text{total}} = \dfrac{12}{4.5} = 2.7\,\Omega$ (2 s.f.)
The total current is the sum of the branch currents. The second branch is an extra path for the charge, so more current flows for the same p.d. — the total resistance is less than the smallest single resistance.

Answer: (a) $1.0\,\text{A}$ and $8.0\,\text{V}$ ; (b) $4.5\,\text{A}$ — the second branch gives the current an extra path, so the total current rises and the total resistance ( $2.7\,\Omega$ ) is less than either resistor.

Question

Stuck on series and parallel circuits?