A capacitor stores energy in an electric field between two conductors separated by a dielectric. An inductor stores energy in a magnetic field created by current through a coil. Their behaviour is complementary: a capacitor opposes a change of voltage, while an inductor opposes a change of current.
Capacitance
Charge and energy in a capacitor
Problem. A 100 µF capacitor is charged to 50 V. Find the stored charge and energy.
Solution. Q = C × V = 100 × 10⁻⁶ × 50 = 5 × 10⁻³ C = 5 mC. E = ½ × 100 × 10⁻⁶ × 50² = 0.5 × 100 × 10⁻⁶ × 2500 = 0.125 J.
Inductance
Voltage across an inductor
Problem. The current through a 10 mH inductor rises from 0 A to 2 A in 5 ms. What average voltage appears across it?
Solution. ΔI/Δt = 2 ÷ 0.005 = 400 A/s. V = L × ΔI/Δt = 0.010 × 400 = 4 V.
- A capacitor blocks steady DC after charging and passes changing signals more readily at higher frequency.
- An inductor passes steady DC and opposes changes of current.
- Both components store energy and can deliver it after the supply is removed.
- Electrolytic capacitors are polarised and must be connected with the correct polarity.
- C = Q/V and E = ½CV² describe a capacitor.
- V = L di/dt and E = ½LI² describe an inductor.
- Capacitors oppose voltage change; inductors oppose current change.
- Both store energy that persists after isolation.
Worked example
A 10 mH inductor carrying 2 A stores E = ½ × 0.010 × 2² = 0.02 J. That energy must be absorbed by a flyback path when the current is interrupted.