What is resonance in a series LCR circuit? Derive the resonant frequency, draw the variation of current with frequency and give one application.

1. 1 · Define. Resonance occurs when X_L = X_C, so Z = R and the current is greatest.
2. 2 · Derive. ω₀L = 1/(ω₀C), so ω₀ = 1/√(LC) and ν₀ = 1/(2π√(LC)).
3. 3 · Draw the graph. [iₘ against ω; two curves peaking at the same ω₀; the taller one labelled small R]
4. 4 · State the features. At ω₀: φ = 0, power factor 1, and the voltages across L and C are equal and opposite.
5. 5 · Real life. Tuning an FM radio to a station uses resonance.
6. 6 · Close in one line. So, the circuit picks out the frequency ω₀ = 1/√(LC).

Scoring tip: Keep both curves peaking at the same ω₀; a shifted peak loses the mark.