Electrical Engineering ⇒ Topic : Step Response of R-L-C Circuit
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David
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STEP RESPONSE OF R-L-C CIRCUIT Figure (a) shows a series R-L-C circuit having zero initial conditions, i.e., initially the circuit was relaxed. Let the switch be closed at t = O. The circuit equation is given by
Figure (a) Series R-L-C circuit ........ (1) The Laplace transform of Eq. (1) can be written as ........... (2) ............ (2a) The three possible solutions for I(s) are as follows: ............. (3) ................ (4) ................... (5) Using Eqs. (4) and (5), Eq. (3) can be written as .............. (6) .............(7) Taking the inverse Laplace transform of Eq. (7), we have ................ (8) Case (iii): Roots are imaginary, i.e.and a and b are complex conjugates
.......... (9) Taking the inverse Laplace transform of Eq. (9), we obtain
............... (10) | |
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