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 *b*are real and *a* ≠ *b* i.e.,

∴ Using Eq. (4.85) ...

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