Capacitance and Capacitors
Capacitance questions test charge storage, capacitor combinations, energy, and transient behaviour. You must apply C = Q/V, combine capacitors correctly, and explain why capacitors block DC while passing AC.
Core rules
- Capacitance C = Q/V, measured in farads (F); 1 F = 1 C/V.
- Parallel plates: C = εA/d; larger area or higher permittivity increases capacitance, greater spacing decreases it.
- Capacitors in parallel add; in series, reciprocals add: 1/C_eq = 1/C1 + 1/C2 + ...
- Energy stored: E = ½CV².
- The time constant τ = RC governs charge and discharge rate; after one τ, about 63% of the final change has occurred.
- Capacitor voltage cannot change instantly; current can. A capacitor blocks steady DC but passes changing AC.
Worked example
A 100 µF capacitor is charged to 50 V. Find the charge and stored energy. Q = CV = 100 × 10^-6 × 50 = 5.0 × 10^-3 C = 5.0 mC. E = ½CV² = 0.5 × 100 × 10^-6 × 50² = 0.125 J. Reasoning: convert microfarads to farads before multiplying; energy uses the square of voltage.
Traps
- Combining series capacitors by direct addition.
- Assuming capacitor voltage can jump instantly.
- Forgetting that a dielectric increases capacitance.
- Using peak rather than RMS voltage when calculating AC capacitor stress without checking the rating.