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
/
  • Oscilloscope

  • Function generator
/
  • Breadboard

  • Inductor
/
  • Resistor

  • jumper wires
/
  • 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 self-inductance. 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

(1)

where is the maximum current through the inductor and  is the time constant. The time constant for a RL circuit is defined as

(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

(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

(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.
  1. Attach the oscilloscope probe between the inductor and resistor and the oscilloscope ground between the square wave generator ground and resistor
  2. Set the function generator to square wave.
  3. Use the function generator output knob to set the peak-to-peak voltage to be about 10 V.
  4. Adjust the oscilloscope voltage and horizontal time scale to obtain a single trace similar to either an exponential decay or growth diagram.
  5. Measure the half-life from the oscilloscope display.
  6. 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 ) / Half-life
(in s)
Circuit 1 – No Rod / 10
Circuit 1 – No Rod / 33
Circuit 1 – No Rod / 100
Circuit 2 – Steel Rod / 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) / Resistance of the
function generator (in )
Circuit I – 10 Ω
Circuit I – 33 Ω
Circuit I – 100 Ω
Average Resistance of the function generator
Time constant
 (in s) / Inductance of the core
with steel rod (in )
Circuit II - Steel Rod

Resistance of 8.2mH inductor is 5.6 ohms.