Question

In the circuit shown below, the switch is closed at t = 0. Applied voltage is v (t) = 400cos (500t + π/4). Resistance R = 15Ω, inductance L = 0.2H and capacitance = 3 µF. Find the roots of the characteristic equation.

(a) -38.5±j1290

(b) 38.5±j1290

(c) 37.5±j1290

(d) -37.5±j1290

The question was posed to me during an online interview.

This interesting question is from Sinusoidal Response of an R-L-C Circuit in section Transients of Network Theory

Answer 1

Right option is (d) -37.5±j1290

Explanation: By applying Kirchhoff’s voltage law to the circuit,

On differentiating the above equation and on solving, we get roots of the characteristic equation as -37.5±j1290.