1.

In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 50cos (102t+π/4), resistance R = 10Ω and capacitance C = 1µF. The complementary function of the solution of ‘i’ is?(a) ic = c exp (-t/10^-10)(b) ic = c exp(-t/10^10)(c) ic = c exp (-t/10^-5)(d) ic = c exp (-t/10^5)The question was posed to me in final exam.Origin of the question is Sinusoidal Response of an R-C Circuit in portion Transients of Network Theory

Answer»

The CORRECT choice is (c) ic = c exp (-t/10^-5)

To elaborate: By APPLYING Kirchhoff’s voltage LAW to the CIRCUIT, we have

(D+1/10^-5) )i=-500sin⁡(1000t+π/4). The complementary FUNCTION is ic = c exp (-t/10^-5).



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