A series circuit contains a 20-Ω resistor, a 200-mH inductor, a 10-μF capacitor, and an ac power source. At what frequency should the power source drive the circuit in order to have maximum power transferred from the driving source?

f = 113 Hz

Explanation:

In order to have maximum power transferred from the driving source, as the RMS voltage doesn't depends on frequency, the current I must be maximum.

This condition is met when the circuit behaves a purely resistive, as the impedance is at a minimum.

Such condition is known as resonance, and it satisfies the following equation:

XL = XC ⇒ ω₀ * L = 1 / ω₀*C, where ω₀, is the angular frequency at resonance.

Solving for ω₀, we have:

ω₀ = 1/√LC = 1/√200*10⁻3 H * 10⁻6F = 707 rad/sec

As we need to find the frequency (in cycles/sec), we need to convert from angular frequency to frequency, as follows:

ω₀ = 2*π*f₀ ⇒ f₀ = ω₀ / 2*π = 707 rad/sec / 2*π rad = 113 Hz