In an L-R-C series circuit, the resistance is 340 ohms, the inductance is 0.400

Question

In an L-R-C series circuit, the resistance is 340 ohms, the inductance is 0.400 henrys, and the capacitance is 1.80×102 microfarads.

Part A

What is the resonance angular frequency 0 of the circuit?

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

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.

Explanation / Answer

here,

1)

angular frequency , w = 1/sqrt(LC)

w = 1/sqrt(0.4 * 1.8 * 10^-8 )

w = 11785.11 rad/s.

2. At this angular frequency, inductive reactance and capacitive reactance mutually cancel.

On the other hand,

voltage across capacitor is given by V = I / w C

Assuming V = 590 V, and solving for I,

I = w* C *V = 1178.51 * 1.8 * 10^-8 * 590

I = 0.125 A

This is the peak value for current.

resistance , R = 340 ohms

Vmax = I * R = 0.125 * 340

Vmax = 42.5 V

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