Question

An RLC series circuit has a resistance of R = 330.0 Ω, an inductance L = 0.2000 mH, and a capacitance C = 32.00 nF. (a) What is the resonant frequency? (b) If the capacitor breaks down for peak voltages in excess of 7.000 × 102 V, what is the maximum source voltage amplitude when the circuit is operated at the resonant frequency?

Answer 1

A)

Frequency, f = (1/2 pi) sqrt (1/LC)

f = (1/2 pi) sqrt (1/(0.0002 x 32 x 10^-9)) = 62.91 kHz

B)

Current, I = 700 x 2 pi x 62911.52 x 32 x 10^-9 = 8.85 A

Xl = 2 pi x 62911.52 x 0.0002 = 79.06 ohm

Xc = 1/ 2 pi x 62911.52 x 32 x 10^-6 = 0.08 ohm

V = 8.85 x sqrt[330^2 + (79.06 - 0.08)^2] = 3002.98 V

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