An RLC circuit includes a 10 ohm resistor, 1.5 microfared capacitor and 50 milli

Question

An RLC circuit includes a 10 ohm resistor, 1.5 microfared capacitor and 50 milli-Hendry inductor connected in series. The capacitor is rated at 1200v, its maximum safe voltage. The circuit is driven by an AC voltage source euqal to V=100sinwt volts.

A) At what frequency is the current in the circuit a maximum?

B) What is the peak current in the circuit at this frequency?

C) What are the voltages across the resistor, capacitor and inductor at this frequency?

D) What is the current in the circuit at 50% of the resonant frequency?

Explanation / Answer

Resistance = R = 10 ohm

Capacitance = C = 1.5 microfarad

Inductance = L = 50 mH

Capacitor maximum safe voltage = 1200 volt.

Source

V = 100Sin(wt)

A). Resonance frequency fo

fo = 1/(42(LC)) = 92.5 Hz.

B). Peak current = peak voltage / Resistance = 100/10 = 10 A

C). Voltage across resistor

VR = 10×10 = 100 volt

Across capacitor

Vc = Xc×I ={1/ (2×92.5×1.5×10-6)}×10 = 114.71 volt

Across inductor

VL = XLI = 2×92.5×50×10-3×10 = 290.60 volt.

D). At 50% frequency

f = 92.5/2 = 46.25 Hz

XL = 2fL = 14.53 ohm

Xc = 1/(2fC) = 2294.13 ohm

Impedence = 2279.6 ohm

Max current = 100/2279.6 = 0.044 A

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