Fig. 4.23 shows a series R–L–C circuit having zero initial conditions i.e., initially the circuit was relaxed. Let the switch K be closed at t = 0.
Fig. 4.23 Series RLC circ
The circuit equation is given by
Taking Laplace transform of Eq. (4.81), we can write
The three possible solution for I(s) are as follows,
Case (i) : Both a and bare real and a ≠ b i.e.,
∴ Using Eq. (4.85) ...