A series RCL circuit contains only a capacitor ( C = 12.4 F), an inductor ( L =

Question

A series RCL circuit contains only a capacitor (C = 12.4 F), an inductor (L = 5.27 mH), and a generator (peak voltage = 93.4 V, frequency = 9.27 x 103 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 = 8.84 x 10-4 s. (b) What is the instantaneous value of the current when t = 8.84 x 10-4 s? Be sure to include the plus and minus signs in the answers if applicable. (Hint: The instantaneous values of the voltage and current are the vertical components of the voltage and current phasors, respectively.) Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

Explanation / Answer

the voltage generator can be given as a sine function as

v(t) = 93.4 * sin(2* pi * 9.27 x 103 *t )

so ,

V at t= t = 8.84 x 10-4 s.

v(t) = 67.5699 V

2) now net impedance XL -Xc

so , we have Z=   2*pi f*L - (1/ 2* pi*f*C ) = 306.95 - 1.38 = 305.57 ohms

now ,

V(t) at t=8 .84 x 10-4 s = 93.4 * sin(2* pi * 9.27 x 103 *t ) = 67.5699 V

so current = V(t) / Z= 67.5699 / 305.57 ohms= 0.2211 A

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