Resonance in an R-L-C Circuit In an L-R-C series circuit, the resistance is 340

Question

Resonance in an R-L-C Circuit In an L-R-C series circuit, the resistance is 340 ohms, the inductance is 0.320 henrys, and the capacitance is 2.00 times 10^-2 microfarads. What is the resonance angular frequency omega_0 of the circuit? Express your answer in radians per second to three significant figures. The capacitor can withstand a peak voltage of 570 volts. If the voltage source operates at the resonance frequency, what maximum voltage amplitude V_max can the source have if the maximum capacitor voltage is not exceeded? Express your answer in volts to three significant figures.

Explanation / Answer

Resonant frequency=1(/LC)1/2

w=1.25×10^4rad/sec

Xc=1/wC=0.4×10^4ohm

Vrms=Irms×Xc

570/0.4×10^4=Irms

Irms=0.1425A

at resonanceZ=R

so Vrms=Irms×R=0.1425×340=48.45V

Vmax=48.45×1.414=68.51V

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