Problem 7: For the same RLC series circuit having a 40.0 Ω resistor, 3.00 mH inductor and a 5.00 μF capacitor: (a) Find the resonant frequency (b) calculate Irms at resonance if Vrms is 120 V.

Solution

(a) Given

L = 3.0 mH = 3 × 10^{-3} H, C = 5.0 μF = 5.0 × 10^{-6}F

Asked

Resonant frequency, f_{r}.

Formula

Put the values

(b) Given

R = 40 Ω V_{rms} = 120 V

Asked: I_{rms}

Formula

However in case of resonance, X_{L} = X_{C}, therefore,
Z = R =40 Ω

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