Derive the expressions for the equivalent capacitance of three capacitors connected (a) in series and (b) in parallel. Find the equivalent capacitance of 2 μF, 3 μF and 6 μF in series.

1. 1 · Define capacitance. C = Q/V; unit farad (1 F = 1 C V⁻¹).
2. 2 · Draw both circuits. [Series: three capacitors in one line across a battery, with +Q and −Q on each. Parallel: three capacitors between two common wires across a battery]
3. 3 · Series derivation. Same Q on each; V = Q/C₁ + Q/C₂ + Q/C₃ = Q/C, so 1/C = 1/C₁ + 1/C₂ + 1/C₃.
4. 4 · Parallel derivation. Same V across each; Q = C₁V + C₂V + C₃V = CV, so C = C₁ + C₂ + C₃.
5. 5 · Numerical. 1/C = 1/2 + 1/3 + 1/6 = 1, so C = 1 μF.
6. 6 · Real life. A ceiling fan uses a capacitor of a few microfarads to start and run smoothly.
7. 7 · Close in one line. Series lowers capacitance below the smallest; parallel raises it above the largest.

Scoring tip: Write 'same charge' for series and 'same potential difference' for parallel before any equation. These two phrases carry marks.