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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»

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).



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