The generator voltage in the RLC circuit alternates at angular frequency omega =

Question

The generator voltage in the RLC circuit alternates at angular frequency omega = 400 rad/s, inducing current 6 A (rms, like all ac variables in this problem) The resistance is R = 15 Ohm and the reactances are X_L = 26 Ohm and X_C = 6.0 Ohm. (a) Find the inductance, the capacitance, the generator voltage V_G, the phase angle by which this voltage leads/lags the current, and the average power. (b) What is the voltage across L and C together? across L and R together? (c) Find the angular frequency at which the current is maximal, and evaluate this current and its phase with fixed emf from part (a).

Explanation / Answer

w = 400 rad/s , I = 6 A, R = 15 ohms ,

XL = 26 ohms , XC = 6 ohms

(a) XL = wL

26 = 400*L

L = 0.065 H

XC = 1/wC

6 = 1/(400*C)

C = 416 uF

V = I*( (R^2 +(XL -XC)^2)^0.5

V = 6 (15^2 +(26-6)^2)^0.5

V = 150 V

cos(phi) = R/Z

phi = arccos(15/((15^2 +(26-6)^2)^0.5))

phi = 53 degrees

Pavg = IVcos(phi)

P = 150*6*cos(53)

P = 541.6 W

(b) in series combination current is constant

VL = xL*I , VC = XC*I

VLC = I (XL -XC) = 6(26-6) = 120 V

VLR = 6*(15^2 +26^2)^0.5 = 180.1 V

(c) w^2 = 1/LC

w^2 = 1/(0.065*416*10^-6)

wR = 192 rad/s

Irms = V/R = 150/15 = 10 A

Imax = 10*1.414 = 14.14 A

phi' = 0

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