Resonance in an RLC Circuit In an LRC series circuit the res

Resonance in an R-L-C Circuit In an L-R-C series circuit, the resistance is 300 ohms, the inductance is 0.360 henrys, and the capacitance is 1.60×102 microfarads.

Part A

What is the resonance angular frequency 0 of the circuit?

Express your answer in radians per second to three significant figures.

0 =_________________ rads/s

Part B

The capacitor can withstand a peak voltage of 590 volts. If the voltage source operates at the resonance frequency, what maximum voltage amplitude Vmax can the source have if the maximum capacitor voltage is not exceeded?

Express your answer in volts to three significant figures.

Vmax =_________________ V

Solution

w₀ = 1 / sqrt (0.360 * 1.6 * 10-8)

= 1 / sqrt (L C)

= 13176 rad/s = 1.31 * 10⁴ rad/s

----------------------------------------------.

X_C = 1 / (wC) = X_L = w L = 4743 ohms

Z = R = 300 ohms.

Assume 1 V is applied to circuit , I = V / Z = 1 / 300 = 0.0033 A

V_C = I* X_C = 0.0033 * 4743 = 15.8 V

V_max = 1 * 590/ 15.8

= 37.35 V