RL Circuits
Objective:
 To study the behavior of an RL circuit
 To determine the time constant of an RL circuit
 To determine the inductance of an unknown inductor
Apparatus:
 PASCO circuit board
 Function generator
 Inductor
 jumper wires




Oscilloscope
Breadboard
Resistor
alligator clips
Introduction and Theory:
Inductor is a coil of wire and is used to store magnetic field. A magnetic field is generated in an
inductor as current passes through it. As the magnetic field increases in the coil, an induced
magnetic field is created in the opposite direction in the coil. This is referred to as selfinductance. The measure of self-inductance is known as inductance. As long as there is a change
in the current, a magnetic field will be induced in accord with Faraday’s law of induction. If the
current reaches a maximum value and becomes constant, as in DC circuits, then the induced
magnetic field will become zero. If a resistor is connected in series with an inductor, then the
behavior of the circuit is very similar to that of a RC circuit. The current through the inductor in
an RL circuit is given by

i (t )  I 0 1  e  t / 

(1)
where I 0 is the maximum current through the inductor and  is the time constant. The time
constant for a RL circuit is defined as
 
L
R
(2)
If the current is initially zero, then the time constant represents the time required for the current
to reach 63.2% of the maximum current. If the initial current is at maximum value, then the time
constant will represent the time required for the current to drop to 37.8% of the initial value.
Rather than measuring the current through the inductor, it is much simpler to measure the
potential difference across the resistor. The variation of voltage across the resistor is similar to
the variation of the current in the inductor. From Ohm’s law, the voltage drop across the resistor
is given by

v(t )  V0 1  e  t / 

(3)
The “half-life” is the time required for the RL circuit’s voltage to reach half of its maximum
value.
In terms of the time constant, the half-life is
t1 / 2 
L
ln 2
R
(4)
By measuring the half-life, either the inductance of an unknown inductor or the resistance of an
unknown resistor can be found.
Procedure:
1. Use multimeter to measure and record the actual resistances of the 100  resistor and that of
the 8.2 mH inductor.
2. Using a PASCO circuit board, create the circuit shown below.
L
+

R
V
Oscilloscope
3. Attach the oscilloscope probe between the inductor and resistor and the oscilloscope ground
between the square wave generator ground and resistor
4. Set the function generator to square wave.
5. Use the function generator output knob to set the peak-to-peak voltage to be about 10 V.
6. Adjust the oscilloscope voltage and horizontal time scale to obtain a single trace similar to
either an exponential decay or growth diagram.
7. Measure the half-life from the oscilloscope display.
8. Now place the steel rod inside the inductor core and repeat the
Data Sheet:
Resistance of the inductor = _________________________
Frequency
(in Hz)
Resistance of the
Resistor
(in )
Circuit 1 – No
Rod
Circuit 1 – No
Rod
Circuit 1 – No
Rod
Circuit 2 –
Steel Rod
Half-life
(in s)
10
33
100
10
Calculations:
1. Calculate the time constant for the RL circuit.
2. Using the half-life information from the first part, calculate the average actual resistance of
the function generator.
3. Calculate the inductance of the inductor with steel core.
Results:
Time constant
 (in s)
Circuit I – 10 Ω
Circuit I – 33 Ω
Circuit I – 100 Ω
Average Resistance of the function
generator
Resistance of the
function generator (in )
Time constant
 (in s)
Circuit II - Steel
Rod
Resistance of 8.2mH inductor is 5.6 ohms.
Inductance of the core
with steel rod (in )