Page 237 - Basic Electrical Engineering

2.10.1 Introduction

When a circuit containing inductance, capacitance, and resistance is switched
on to a dc supply, the time taken for the current to attain a steady-state

condition is called its transient response or transient time. Let a circuit
contain a resistance and an inductance or a capacitance connected across a dc

source of supply through a switch. When the switch is turned on, the current
does not immediately reach its final value. Both the inductance and the

capacitance are energy-storing elements. In an inductance, energy is stored in
the form of a magnetic field, whereas in a capacitor energy is stored in the
form of an electric field. Initially, the current flows at a high rate but as the

energy-storing elements, i.e., either the inductor or the capacitor stores more
and more energy, the rate of flow of current decreases, and a steady state is

reached. Thus transient response is studied when a circuit containing
inductance and/or capacitance is switched on and switched off. Unlike a

purely resistive circuit, R–L or R–C circuit solutions during the transient
condition will involve the solution of differential equations and not algebraic

equations. Transient response of an R–L circuit and an R–C circuit are
discussed in this section.

2.10.2 Transient in R–L Circuit

In Fig. 2.161 is shown an inductor of L Henry connected in series with a
resistance of R Ω. The combination is connected to a source of supply, V.

When a two-way switch S connected to terminal 1, the circuit is on and when
the switch is connected to terminal 2, the supply voltage is cut off and the R–
L circuit gets short circuited. Let at time t = 0, the switch S be connected to

terminal 1. The supply voltage V will be the sum of the voltage drop across
the resistance and the voltage developed across the inductor. So we can write