Refer to Interactive Solution 23.27 for help with problems like this one. A seri

Question

Refer to Interactive Solution 23.27 for help with problems like this one. A series RCL circuit contains only a capacitor (C = 11.8 mu F), an inductor (L = 3.69 mH), and a generator (peak voltage = 65.4 V, frequency = 8.20 times 10^3 Hz). When t = 0 s, the instantaneous value of the voltage is zero, and it rises to a maximum one-quarter of a period later. (a) Find the instantaneous value of the voltage across the capacitor/inductor combination when t = 3.49 times 10^-4 s. (b) What is the instantaneous value of the current when t = 3.49 times 10^-4 s? Be sure to include the plus and minus signs in the answers if applicable.

Explanation / Answer

V(t) = Vo*sin2pi*f*t

Vo = 65.4 V

f = 8.2 x 10^3 Hz

t = 3.49 x 10^-4 s

V(t) = -49.92 V

part b )

XL = 2pif*L = 190.12 ohm

Xc = 1/2pifC = 1.645 ohm

XL > Xc so current lags the voltage by pi/2 radians

I(t) = Io*sin(2pift - pi/2)

Io = Vo/Z

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

Z = 188.475 ohm

Io = 0.347 A

I(t) = 0.098 A

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