Electricity 2 — AC Circuits

Resonance

continues from lesson 3 — values defined earlier in the course stay live here

Sweep the frequency and there is exactly one point where X_L = X_C — they cancel, impedance collapses to just R, and current peaks. That frequency is the circuit's natural note: f₀ = 1/(2π√(L·C)). Radios tune by moving it.

f_{0} = \frac{1}{2 \cdot \pi \cdot \sqrt{L_{1} \cdot C_{1}}}

= 159.15 Hz resonant frequency — about 159 Hz here

✓ pass

abs(2 * \pi * f_{0} * L_{1} - 1 / (2 * \pi * f_{0} * C_{1})) < 0.001 ohm

at f₀ the reactances really cancel

sqrt(100^2 + (2 * pi * x * 0.05 - 1 / (2 * pi * x * 20e-6))^2)

impedance vs frequency (Hz) — the dip at ≈159 Hz is resonance

Where next: AC Motors puts these ideas to work — three AC waves, 120° apart, spinning real machinery.