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(12) (CIRCLE YOUR FINAL ANSWER with Unit) A series LCR circuit has resistance R-

ID: 2038803 • Letter: #

Question

(12) (CIRCLE YOUR FINAL ANSWER with Unit) A series LCR circuit has resistance R-500 ? , inductance L input AC voltage is Vin-150006 (w t ) Volt, where-2 4 ? F , if the ? f , and frequency f of AC voltage is 1 H , capacitor C w= 60 Hz. Find the inductive reactance (X -WL) (1+1 points), capacitive reactance (X-1/wC) (1+1 points) RMS current in the circuit (4+1 points), phase angle between voltage and current (4 points) For what frequency the impedance will be 500 ? , at that frequency current lead, the voltage , in phase or , lags the voltage? (5+2 points)

Explanation / Answer

xL = w L = (2 pi f) L

XL = (2 x pi x 60) (1) = 377 ohm .....Ans


Xc = 1 /(2 pi f C) = 1/(2 x pi x 60 x 4 x 10^-6)

Xc =663 ohm ....Ans


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

Z = sqrt[ 500^2 + (663 - 377)^2] = 576 ohm

Imax = V / Z = 150 / 576 = 0.260 A  


Irms = Imax / sqrt(2) = 0.184 A .....Ans


tan(phi) = [ (XL - XC)/R] = - 0.576

phi = - 30 deg ......Ans

Z = R = 500ohm when XL = XR

2 pi f L = 1 / (2 pi f C )

f = 1 / (2 pi sqrt(LC)) = 79.6 Hz ......Ans

phi = 0

so voltage and current are in phase. .....Ans