An A.C. generator which produces an e.m.f. of e = e 0 sin(?t) , where e0 = 25 V

Question

An A.C. generator which produces an e.m.f. of e = e 0 sin(?t) , where e0 = 25 V and ? =
377 rad s-1 and is connected to a 4.15 µF capacitor.
a. What is the maximum value of the current flowing in the circuit?
b. When the current is a maximum, what is the e.m.f. of the generator?
c. When the e.m.f. of the generator is -12.5 V and increasing in magnitude (i.e.
becoming more negative), what is the current?
The capacitor in the circuit is replaced with a 12.7 H inductor.
d. What is the maximum value of the current flowing in the circuit?
e. When the current is a maximum, what is the e.m.f. of the generator?
f. When the e.m.f. of the generator is -12.5 V and increasing in magnitude (i.e.
becoming more negative), what is the current?
explain your answer and make it is clear as possible as you can

Explanation / Answer

Data: E = Eo sin t Eo = 25 V = 377 rad/s Capacitance, C = 4.15 x 10^-6 F Inductance, L = 12.7 H Solution: (a) Imax = Eo / Z          = Eo / Xc          = Eo / ( 1 / C )          = Eo C          = 25 * 377 * 4.15 x 10^-6          = 39.1 x 10^-3 A (b) Emf of the generator corresponding to max current = 0 (c) E / Eo = sin t - 12.5 / 25 = sin t - 1/2 = sin t t = 210 deg      = 7 / 6 rad Here, current leads voltage by /2 rad Hence, I = Io sin (t + /2)               = 39.1 x 10^-3 * sin ( 7/6 + /2 )               = 39.1 x 10^-3 * sin 5/3               = 33.9 x 10^-3 A (d) Imax = Eo / Z          = Eo / XL          = Eo / L          = 25 / 377 * 12.7          = 5.22 x 10^-3 A (e) Emf of the generator corresponding to max current = 0 (f) E / Eo = sin t - 12.5 / 25 = sin t - 1/2 = sin t t = 210 deg      = 7 / 6 rad Here, current lags voltage by /2 rad Hence, I = Io sin (t - /2)               = 5.22 x 10^-3 * sin ( 7/6 - /2 )               = 5.22 x 10^-3 * sin 5/3               = 4.52 x 10^-3 A (d) Imax = Eo / Z          = Eo / XL          = Eo / L          = 25 / 377 * 12.7          = 5.22 x 10^-3 A (e) Emf of the generator corresponding to max current = 0 (f) E / Eo = sin t - 12.5 / 25 = sin t - 1/2 = sin t t = 210 deg      = 7 / 6 rad Here, current lags voltage by /2 rad Hence, I = Io sin (t - /2)               = 5.22 x 10^-3 * sin ( 7/6 - /2 )               = 5.22 x 10^-3 * sin 5/3               = 4.52 x 10^-3 A (e) Emf of the generator corresponding to max current = 0 Emf of the generator corresponding to max current = 0 (f) E / Eo = sin t - 12.5 / 25 = sin t - 1/2 = sin t t = 210 deg      = 7 / 6 rad Here, current lags voltage by /2 rad Hence, I = Io sin (t - /2)               = 5.22 x 10^-3 * sin ( 7/6 - /2 )               = 5.22 x 10^-3 * sin 5/3               = 4.52 x 10^-3 A E / Eo = sin t - 12.5 / 25 = sin t - 1/2 = sin t t = 210 deg      = 7 / 6 rad Here, current lags voltage by /2 rad Hence, I = Io sin (t - /2)               = 5.22 x 10^-3 * sin ( 7/6 - /2 )               = 5.22 x 10^-3 * sin 5/3               = 4.52 x 10^-3 A

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