Question

In an LRC series circuit, the inductance is 244 mH, the resistance is 29 Ω, and the capacitance is 354 μF. If the AC voltage applied across the circuit is given by

V(t) = (12 V)sin(11πt)

calculate the voltage across each element at a time of t = 0.04 s.

VR	=	V
VC	=	V
VL	=	V

Answer 1

here given

V(t) = 12 sin 11 pi t

W = 11pi = 11*3.14 = 34.54 rad/s

inductance reactance XL = WL

XL = 34.54 *0.244 = 8.42 ohms

Capactivie reactance Xc = 1/wC

Xc = 1/(34.54 * 354*10^-6)

Xc = 81.78 ohms

impedence Z^2 = R^2 + (Xc-xL)^2

Z^2 = 29^2 + (81.78 -8.42)^2

Z = 78.88 ohms

Voltage at t= 0.04 sec is

V 12* sin(11*3.14 * 0.04)

V = 0.289 Volts

Current I = V/Z = 0.289/78.88 = 3.6 mA

Vr = I R = 0.0036* 29 = 0.106 Volts

VL = iXL = 0.0036 * 8.42 = 0.0303 Volts

Vc = iXc = 0.0036 * 81.78 = 0.294 Volts