A series RCL circuit contains only a capacitor (C = 11.8 mu F), an inductor (L =

Question

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. Find the instantaneous value of the voltage across the capacitor/inductor combination when t = 3.49 times 10^-4 s. 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. The ac current and voltage are rms values and power is an average value unless indicated otherwise. Number units Number units

Explanation / Answer

Since the capacitor and inductor are connected in series, The instantaneous voltage across the combination will be the

source voltage. Vs = Vpeak sin (wt)

omega, w = 2*pi*f, f = 8.2kHz

       w = 51522.12 rad/s

Therefore, at t = 3.49 x 10-4s, wt = 18 rads = 10310

Therefore, instantaneous voltage Vs = 65.4 sin (10310 ) = -49.11 V

XL = 2*pi*f*L = 190.11 ohms

XC = 1/(2*pi*f*C) = 1.6448 ohms

Since XL > XC, Total impedance, Z = j (190.11 - 1.6448) = j 188.465 ohms.

Therefore, instantaneous current, I = instantaneous voltage/ Z = -0.2605 -900 A = 0. .2605 900 A

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