RL Circuit

Title : RL Circuit

Apparatus :

Science Workshop Interface 750 1

Voltage sensor ( PASCO CI-6503 ) 2

Variable Resistor ( 0 - 100 ohms ) 1

Inductors ( 240-turn coil with two soft-iron C-cores ) 1

Objective :

1. Study the growth of current in an RL circuit.

2. Study the induced e.m.f. in an RL circuit during sudden power on and

switch off.

3. Study the inductive time constant, L / R, and inductance of the coil plus

core.

Theory :

Self-induction

The flux due to the current in the coil links that coil and if the current changes the resulting flux change induces an e.m.f. in the coil itself. The process is called self-induction

If the e.m.f. induced in the coil is , when the rate of change of current in it is ,

the inductance L of the coil is defined by the equation

The RL ( d.c. ) circuit

Switching On

Figure 1

When S is closed, the current build-up is opposed by the back e.m.f. induced in the coil, and the current takes a considerable time to reach its equilibrium value.

In the case, I = 0 when t = 0

The solution to the above equation can be shown to be

.......... (1) where

is known as the time-constant of the circuit. The inductive time constant is a measure of how long it takes the current to be established. Remember that R is the total resistance of the circuit and therefore must include the resistance of the coil as well as the resistance of the resistor.

When the switch S is closed, current, I , in the circuit rises exponentially from zero and becomes steady.

Since the voltage across a resistor is given by , the voltage across the resistor rises exponentially.

Since the voltage across an inductor is given by , the voltage across the inductor starts at its maximum value and then decreases exponentially.

Switching Off

If the circuit is switched off, the current would fall to zero suddenly. Since the voltage across L depends on , a large e.m.f. is induced in the inductor. The rate of decrease in magnetic flux is large and the change in magnetic flux is opposite to that when closing S.

Using a Square Wave instead of manual switching

Figure 2

At the rising edge of the square wave, the current rises exponentially and the voltage across L decreases exponentially. This is the same as closing S in Figure 1.

At the falling edge, the applied voltage becomes zero. This is equivalent to the following circuit.

It is not the same as switching off S in Figure 1. Instead of having no current as shown in Figure 1, a current would be registered flowing in the same direction as before.

Calculation of self-inductance, L of the coil

At the rising edge of the square wave

When , .

Substituting the above expressions into equation (1) and solving the equation,

The same expression is obtained at the falling edge of the square wave.

Procedure :

Hardware setup :

1. Connect the Interface to the Computer, turn on the interface, and turn on the computer.

2. Connect the Voltage Sensor to the interface

3. Connect the function generator ( OUTPUT ports on the interface ) directly across the RL

circuit and voltage sensor from analog channel A across the inductor and voltage sensor

from analog channel B across the resistor as shown in Figure 2.

Use the "Output" feature of the interface to supply a voltage to the resistor - inductor circuit.

Software setup :

Experiment 1 : Manual switching on and off

The signal generator is set to output a 5 volt DC.

Experiment 2 : Using a Square Wave instead of manual switching

The signal generator is set to output a 5 volt, "positive only" square wave at 0.4 Hz.

The Signal Generator is set to ' Auto' so it will start and stop automatically.

Data Recording :

Manual switching on and off :

Use a multimeter to measure the resistance of the inductor coil and the resistance of the resistor.

Click the Record (REC) button to begin recording data.

Press the push button immediately after clicking the REC button.

Using a Square Wave instead of manual switching :

Begin data recording by clicking the REC button.

Data sampling would stop automatically in 6 s.

Data Analysis :

Study the growth of current and induced e.m.f in an RL circuit

Study the induced e.m.f. in an RL circuit using square waves

Study the inductive time constant, L / R, in RL circuit

Calculation of inductance

Discussion :

1. What are the precautions of this experiment ?

2. Discuss the sources of error in the above experiments.

3. What are the difficulties in performing the above experiment using

traditional apparatus ?

4. In switching on the circuit, the p.d. across the resistor does not rise

to the maximum output voltage. Suggest a reason for this.