Question

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 = [(3.53-4.99×10^-3)cos⁡(π/4+89.94^o)] exp⁡(-t/0.00001)+4.99×10^-3)  cos⁡(100t+π/2+89.94^o)

(b) i = [(3.53+4.99×10^-3)cos⁡(π/4+89.94^o)] exp⁡(-t/0.00001)+4.99×10^-3)  cos⁡(100t+π/2+89.94^o)

(c) i = [(3.53+4.99×10^-3)cos⁡(π/4+89.94^o)] exp⁡(-t/0.00001)-4.99×10^-3)  cos⁡(100t+π/2+89.94^o)

(d) i = [(3.53-4.99×10^-3)cos⁡(π/4+89.94^o)] exp⁡(-t/0.00001)-4.99×10^-3)  cos⁡(100t+π/2+89.94^o)

The question was asked by my college professor while I was bunking the class.

I need to ask this question from Sinusoidal Response of an R-C Circuit topic in division Transients of Network Theory

Answer 1

Correct option is (a) i = [(3.53-4.99×10^-3)cos⁡(π/4+89.94^o)] exp⁡(-t/0.00001)+4.99×10^-3)  cos⁡(100t+π/2+89.94^o)

Explanation: The complete solution for the current is the sum of the complementary function and the particular integral. So, i = [(3.53-4.99×10^-3)cos⁡(π/4+89.94^o)] exp⁡(-t/0.00001)+4.99×10^-3)  cos⁡(100t+π/2+89.94^o).