ABSTRACT
At the end of this chapter you should be able to:
• determine the transient response of currents and voltages in R-L, R-C and L-R-C series circuits using differential equations
• define the Laplace transform of a function • use a table of Laplace in electrical engineering for transient analysis
of simple networks • use partial fractions • deduce expressions in the s-plane given initial conditions • use Laplace diagrams in the s-plane • deduce Kirchhoff’s for determining the response of R-L, R-C and L-R-C
networks, given • explain the response is over, critical, under or zero-damped and
calculate circuit • predict the circuit given non-zero initial conditions
A transient state will exist in a circuit containing one or more energy storage elements (i.e. capacitors and inductors) whenever the energy conditions in the circuit change, until the new steady state condition is reached. Transients are caused by changing the applied voltage or current, or by changing any of the circuit elements; such changes occur due to opening and closing switches. Transients were introduced in Chapter 19 where growth and decay curves were constructed and their equations stated for step inputs only. In this chapter, such equations are developed analytically by using both differential equations and Laplace transforms for different waveform supply voltages.
