The inductance of a tuning circuit of an AM radio is 4 mH. Find the capacitance of the circuit required for reception at 1200 kHz.

A tuning circuit receives a signal at its resonant frequency: f = 1 ÷ (2π√(LC)). Making C the subject gives C = 1 ÷ (4π²f²L).

f = 1200 kHz = 1.2 × 10⁶ Hz, so f² = 1.44 × 10¹². L = 4 × 10⁻³ H.

4π² = 39.48. So 39.48 × 1.44 × 10¹² × 4 × 10⁻³ = 2.27 × 10¹¹.

C = 1 ÷ 2.27 × 10¹¹ ≈ 4.4 × 10⁻¹² F = 4.4 pF.