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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 complete solution of ‘i’ is?(a) i = c exp (-t/10^-5) – (4.99×10^-3) cos⁡(100t+π/2+89.94^o)(b) i = c exp (-t/10^-5) + (4.99×10^-3) cos⁡(100t+π/2+89.94^o)(c) i = -c exp(-t/10^-5) + (4.99×10^-3) cos⁡(100t+π/2+89.94^o)(d) i = -c exp(-t/10^-5) – (4.99×10^-3) cos⁡(100t+π/2+89.94^o)The question was asked in an online interview.I'm obligated to ask this question of Sinusoidal Response of an R-C Circuit topic in division Transients of Network Theory

Answer»

The CORRECT OPTION is (b) i = c exp (-t/10^-5) + (4.99×10^-3) cos⁡(100t+π/2+89.94^o)

EASY explanation: The COMPLETE solution for the current is the sum of the complementary function and the particular integral. The complete solution for the current becomesi = c exp (-t/10^-5) + (4.99×10^-3)cos⁡(100t+π/2+89.94^o).



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