Question

In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 100cos (103t+π/2), resistance R = 20Ω and inductance L = 0.1H. The complete solution of ‘i’ is?

(a) i = ce^-200t + 0.98cos⁡(1000t-π/2-78.6^o)

(b) i = ce^-200t + 0.98cos⁡(1000t+π/2-78.6^o)

(c) i = ce^-200t + 0.98cos⁡(1000t+π/2+78.6^o)

(d) i = ce^-200t + 0.98cos⁡(1000t-π/2+78.6^o)

I had been asked this question during an online interview.

I would like to ask this question from Sinusoidal Response of an R-L Circuit topic in portion Transients of Network Theory

Answer 1

Right choice is (b) i = ce^-200t + 0.98cos⁡(1000t+π/2-78.6^o)

Easiest explanation: The complete solution for the current is the sum of the complementary function and the particular integral. The complete solution for the current becomes  i = ce^-200t + 0.98cos⁡(1000t+π/2-78.6^o).