A series RCL circuit contains only a capacitor ( C = 7.39F), an inductor ( L = 3

Question

A series RCL circuit contains only a capacitor (C = 7.39F), an inductor (L = 3.90 mH), and a generator(peak voltage = 58.6 V, frequency = 5.53 x 103Hz). When t = 0 s, the instantaneous value of the voltageis zero, and it rises to a maximum one-quarter of a period later.(a) Find the instantaneous value of thevoltage across the capacitor/inductor combination when t =3.56 x 10-4 s. (b) What is theinstantaneous value of the current when t = 3.56x 10-4 s? (Hint: The instantaneous values of thevoltage and current are the vertical components of the voltage andcurrent phasors, respectively.) Note: The ac current andvoltage are rms values and power is an average value unlessindicated otherwise.

Explanation / Answer

(a)    the instantaneous value of the voltage at atime of t = 3.56 x 10-4 s will be    V(t) = Vo sin 2 f t           =......... V (b)    the inductive and capacitive reactancesare    XL = 2 f L    XC = 1 / 2 f C    Z = [R2 + (XL -XC)2]    the instantaneous current will be    I = (Vo / Z) sin (2 f t -(1 / 2) )      = ........ A    V(t) = Vo sin 2 f t           =......... V (b)    the inductive and capacitive reactancesare    XL = 2 f L    XC = 1 / 2 f C    Z = [R2 + (XL -XC)2]    the instantaneous current will be    I = (Vo / Z) sin (2 f t -(1 / 2) )      = ........ A

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