In a series oscillating RLC circuit R 160 ohm C 311 micro

In a series oscillating RLC circuit, R = 16.0 ohm, C = 31.1 micro F, L = 9.29 mH, and energy is being supplied by the generator, (b) the rate P_c at which the energy in the capacitor is changing, (c) the rate P_l at which the energy in the inductor is changing, and (d) the rate P_R at which energy is being in the resistor.

Solution

impedence z^2 = R^2 + (XL-xc)^2

inductive reactance XL = wL = 2930 * 0.00929 = 27.21 ohms

Capacitive reactance Xc = 1/wC = 1/(2930 * 31.1 e -6) = 10.97 ohms

Impedence Z^2 = 16^2 + (27.21 - 10.91)^2

Z = 22.84 ohms

Current I = V/Z = 44.6/22.84 = 1.952 Amps

V at time t = 0.444 secs is

V = 44.6 sin (2930 * 0.444)

V = 13.2 Volts

power factor cos theta = R/Z = 16/22.84 = 0.7

Power across Generator = VI cos thwta

Pg = 13.2 * 1.952 * 0.7

Pg = 18.3 Watts
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Pc = V^2 Cos theta /Xc = 13.2*13.2* 0.7/(10.97)

Pc = 11.11 Watts

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PL = V^2 cos theta/XL = 13.2 *13.2* 0.7/(27.21)

Pl = 4.48 Watts

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PR = V^2 Cos theta/R

PR = 13.2*13.2 * 0.7/16

Pr = 7.623 Watts