A series RLC circuit driven by a source with an amplitude of 120.0 V and a frequ

Question

A series RLC circuit driven by a source with an amplitude of 120.0 V and a frequency of 50.0 Hz has an inductance of 782 mH, a resistance of 234 , and a capacitance of 46.4 µF.

(a) What are the maximum current and the phase angle between the current and the source emf in this circuit?

(b) What are the maximum potential difference across the inductor and the phase angle between this potential difference and the current in the circuit?

VL, max

(c) What are the maximum potential difference across the resistor and the phase angle between this potential difference and the current in this circuit?

VR, max

(d) What are the maximum potential difference across the capacitor and the phase angle between this potential difference and the current in this circuit?

VC, max

Explanation / Answer

inductive reactance, XL = 2 pi f L = 2 x pi x 50 x 0.782 = 245.7 ohm

capacitive reactace, Xc = 1 / 2pi f C = 1 /(2 x pi x 50 x 46.4 x 10^-6)

Xc = 68.6 ohm

Z = sqrt[ R^2 + (XL - Xc)^2] = 293.45 ohm

Imax = Vmax / Z = 0.409 A

@ = tan^-1[ (XL - Xc) / R ] = 37.12 deg

b) VL = XL * I = 100.5 volt

90 deg

c) Vr = 234 * 0.409 = 95.71 volt

0 deg

d) Vc= Xc * I = 28.06 Volt

-90 deg

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