Wentworth Institute of Technology
Department of Electronics and Mechanical
ELEC 195 - Circuits Theory II
Name:
Date:
Experiment 4
The Step and Natural Response of an RL Circuit
Objective:
1. To become familiar with the step response of an RL circuit.
2. To become familiar with the natural response of an RL circuit
Equipment Required:
PC with Pspice
Resume of Theory:
The response of a circuit to the sudden application of a constant voltage or current
source is referred to as the step response of the circuit (shown in Fig. 3.1 when the
switch is thrown to position B). In an RL circuit the initial conditions to determine the step
response are assumed to Io. The expressions for the current in the circuit and the
voltage across the inductor after the voltage source is applied are:
i (t ) 
Vs
(1  e t /  )
R
V (t )  Vs * e t / 
The expression for the inductor current indicates that the current increases from zero to a
final value of Vs/R at a rate determined by the time constant  = L/R
Fig. 3.1
A. Khabari
Wentworth Inst. of Tech.
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The currents and voltages that arise when the energy stored in an inductor is suddenly releases
to the resistor when the external source of power stops delivering energy to the circuit (shown in
Fig. 3.1 when the switch is thrown in position A). The expression for the current and voltage
across the resistor are:
i (t )  I o e  t / 
V (t )  I o Re t / 
where Io is the initial current through the inductor before the power source goes off and the
inductor starts releasing energy to the circuit.
Procedure:
Since the step and natural response of an RL circuit occur extremely fast. It would be very hard to
monitor the voltage and current in the circuit and that requires using a high inductance coil. Thus,
the natural and step response of the circuit are studied using a computer simulating software,
Pspice. Using Pspice, simulate the step and natural response of the circuit shown below (Fig.
3.2)
Fig. 3.2
Consider the generic RL circuit shown in Fig. 3.2 below. Unless stated otherwise, we will always
assume that there is no current initially in the circuit. At the time t = 0, The S1 switch is closed
while S2 remains closed and S3 remains open to include the power source in the circuit. Thus
from t = 0s to t = 1s, we can observe the step response of the RL circuit. At t =1s, the power
source is disconnected through S2, and the circuit would be in its natural response.
Using Pspice plot:
1.
2.
3.
4.
A. Khabari
Plot the current I(t) vs. time for 2 seconds
Plot the voltage V(t) vs. time for 2 seconds
Associate your plots to the step and natural response of the RL circuit
Find the time constant of the circuit and mark the time constant in your plot
Wentworth Inst. of Tech.
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