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 = [-0.98 cos⁡(π/2-78.6^o)] exp⁡(-200t)+0.98cos⁡(1000t+π/2-78.6^o)

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

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

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

I have been asked this question during an online interview.

Asked question is from Sinusoidal Response of an R-L Circuit topic in chapter Transients of Network Theory

Answer 1

Correct answer is (a) i = [-0.98 cos⁡(π/2-78.6^o)] exp⁡(-200t)+0.98cos⁡(1000t+π/2-78.6^o)

Easy explanation: The complete solution for the current is the sum of the complementary function and the particular integral.

So, i = [-0.98 cos⁡(π/2-78.6^o)] exp⁡(-200t)+0.98cos⁡(1000t+π/2-78.6^o).