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12 April, 04:38

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?

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  1. 12 April, 04:54
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    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
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