Solved Problems-6

Problems-6
A series R-L-C circuit with R = 3Î©, L = 1H and C = 0.5 F is excited with a unit step voltage. Obtain an expression for the current, using Laplace transform. Assume that the circuit is relaxed initially.
Solution
By KVL,

Since the circuit is initially relaxed,
âˆ´

Putting the values,

or I(s) =

where,

âˆ´

Taking inverse Laplace transform,
i(t) = eâ€“ t + eâ€“2t (A)