Series and parallel circuits
Series and parallel are the two basic ways of connecting components. Each obeys distinct rules for current, potential difference (p.d.) and resistance.
Series circuits
In a series circuit there is only one path for the current.
- Current is the same at every point: I_total = I_1 = I_2 = ...
- P.d. splits across components: V_total = V_1 + V_2 + ...
- Resistance adds: R_total = R_1 + R_2 + ...
If one component breaks, the whole circuit breaks (e.g. old fairy lights).
Parallel circuits
In a parallel circuit each component has its own loop back to the cell.
- Current splits: I_total = I_1 + I_2 + ... (Kirchhoff's first law)
- P.d. is the same across each parallel branch: V_total = V_1 = V_2 = ...
- Resistance of the combination is less than the smallest individual resistance: 1/R_total = 1/R_1 + 1/R_2 + ...
Each branch can switch independently — the basis of household wiring.
✦Worked example— Worked example (parallel)
Two resistors of 6 ohm and 3 ohm in parallel across a 6 V cell.
- 1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, so R = 2 ohm.
- Total current I = V/R = 6/2 = 3 A.
- Each branch sees the full 6 V: I_1 = 6/6 = 1 A, I_2 = 6/3 = 2 A. Branches sum to 3 A — checks.
WJEC exam tip
Always state the rule you are using before the calculation: "In parallel, p.d. across each branch is equal" then plug in the numbers. Examiners credit the rule M1 and the answer A1 separately, so the workings line is non-negotiable.
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