The figure shows an LCR Circuit with R = 60.0 ohm, L = 175 mH, and C = 85.0 micr

Question

The figure shows an LCR Circuit with R = 60.0 ohm, L = 175 mH, and C = 85.0 micro F connected to an ac source that generates a voltage given by: V(t) = 220 V Sin(120 pi t). (i) What is the maximum voltage generated by the source? (ii) What is the frequency of the ac source? (iii) What is the impedance Z of the circuit? (iv) What is the maximum current in the circuit? (v) Calculate the maximum potential drop V_R across the resistor, V_L inductor and V_c capacitor respectively (vi) What is the phase angle phi?

Explanation / Answer

(i) Maximum voltage, Vmax = 220 V

(ii) Frequency, f = / 2 = (120) / 2 = 60 Hz

(iii) XL = L = 120 * 0.175 = 66.0 ohm

XC = 1/C = 1 / [120 * (85 * 10-6)] = 31.2 ohm

So, Impedence, Z = [R2 + (XL - XC)2]1/2 = [60.02 + (66.0 - 31.2)2]1/2 = 69.4 ohm

(iv) Maximum current, Imax = Vmax/Z = 220 / 69.4 = 3.17 A

(v) VR,max = ImaxR = 3.17 * 60.0 = 190 V

VL,max = ImaxXL = 3.17 * 66.0 = 209 V

VC,max = ImaxXC = 3.17 * 31.2 = 98.9 V

(vi) Phase angle, = tan-1[(XL - XC)/R] = tan-1[(66.0 - 31.2) / 60.0] = 30.1o

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