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Signals and Systems by Smarajit Ghosh

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4.19 STEP RESPONSE OF SERIES R–L–C CIRCUIT

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.

 

Series RLC circ

 

Fig. 4.23 Series RLC circ

 

The circuit equation is given by

 

image

 

Taking Laplace transform of Eq. (4.81), we can write

 

image

 

The three possible solution for I(s) are as follows,

Case (i) : Both a and bare real and ab i.e.,

 

 

 

∴ Using Eq. (4.85) ...

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