ECED 2000 Electric Circuits
Laboratory 7 – First Order Systems
Prior to arriving at the laboratory to carry out this experiment analyze the circuits shown
in Parts I and II to determine the time constants of the respective circuits. Enter your
calculations in the table shown below under the heading “Calculated”.
Circuit
Part I, B
Part I, C
Part I, D
Calculated
Time Constant
Measured
Time Constant
% Difference
Part II, A
Part II, B
NOTE:
1. Remember that for a capacitive circuit the time constant is given by RC where R and C are
the values of equivalent resistance and capacitance obtained after the circuit has been
reduced to one capacitor and one resistor (R = Rth seen by the capacitor).
2. The time constant of an RL circuit is given by L/R where L and R are the values of the L and
R arrived at when the circuit has been reduced to one value of each of these components
(R = Rth seen by the inductor).
Dalhousie University
Department of Electrical & Computer Engineering
ECED 2000 Electric Circuits
Laboratory 7 – First Order Systems
Object:
To become familiar with the transient behavior of first order circuits
Apparatus/Equipment:
Resistors:
three (3) 100 
two (2) 100 k
two (2) 0.01 F
one (1) 10 mH
one (1)
one (1)
one (1)
one (1) – dual trace
one (1) – both + and – D.C. voltage
one
Capacitors:
Inductor:
Breadboard:
Digital Multimeter:
Square Wave Generator:
Oscilloscope:
Power Supplies:
Op-Amp:
Procedure:
Part I:
As outlined below
Transients in RC Circuits
Set up the RC circuit as shown in the circuit diagram below.
+12 V
3
741
2
V in
100 k 
7
S2
6
S1
4
-12 V
100 k 
C1
0.01 F
0.01F
A. With switch S1 and S2 open, apply to the circuit shown above a two (2) volt peak-to-peak
square wave with a frequency that allows estimating the circuit time constant τ.
Suggestion: Make the square wave have a period of at least ten (10) times the time constant τ
of the circuit. Good estimates of final values 𝑣(∞) are found for half period ≥ 5τ.
𝜏 can then be estimated as the time interval (𝑡 − 𝑡0 ) for which:
(a) 𝑣(𝑡) − 𝑣(𝑡0+ ) = 0.632(𝑣(∞) − 𝑣(𝑡0+ )), OR
(b) 𝑣(𝑡) − 𝑣(∞) = 0.368(𝑣(𝑡0+ ) − 𝑣(∞))
in any half period where 𝑡0 marks the beginning of the half period interval.
B. Using the dual-trace oscilloscope, observe the applied voltage and the voltage across the
capacitor C1. Carefully sketch the superimposed waveforms.
C. Repeat A) and B) with switch S1 closed.
D. Repeat A) and B) with switch S1 and S2 closed.
Part II:
Transients in RL Circuits
Set up the RL circuit as shown in the circuit diagram given below.
+12 V
3
7
741
2
100 
100 
6
4
-12 V
S1
10 mH
100
A. With switch S1 closed, apply to the circuit shown a two (2) volt peak-to-peak square wave
with a frequency that allows estimating the circuit time constant τ.
B. Repeat A) with switch S1 open.
Results:
I.
Carefully sketch the observed waveforms.
II. Determine the circuit time constants from the response curves.
III. Compare calculated values with the experimental values.