Physics 220 (Section 1)
Lab #11 -- LR Circuits

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Note: Items in red are measurements that must be made as you do the experiment.

 

Introduction

You will both predict and measure the time constant with which an inductor (L) discharges its stored energy through a resistor (R). When the switch connects the battery to the circuit, an application of Kirchoff’s voltage law to the circuit in Figure 1 yields:

  Eq. 1

The current rises from zero and approaches its final value V0 / R,  according the equation:

  Eq. 2

Figure 1

Once the final current is (nearly) obtained, we flip the switch to the lower position. The inductor keeps current flowing through the circuit according to the equation:

  Eq. 3

where t  is no measured from the time we flip the switch downward.

Instead of using a switch, however, we will connect the inductor and resistor to a square wave from a signal generator. Note the square wave is essentially the same thing as a switch that automatically turns a D.C. current on and off -- with the current first going one direction and then the opposite direction.

Voltages as a Function of Time

In order to observe how the voltages across the power supply (signal generator), resistor, and inductor vary in time, we will use an oscilloscope. The following indicates where you need to connect the leads of the oscilloscope to see the voltages across each circuit element:

  1. Signal generator: A and C
  2. Inductor: C and B
  3. Resistor : B and A

Which trace in Figure 2 matches the voltage that you observe across these elements.

   Signal generator:

   Inductor:           

   Resistor:            

Figure 2

LR Time Constant

You can determine the current in the circuit as a function of time from oscilloscope measurements of the decaying voltage across the resistor.  The time constant t (tau) of the circuit is the time required for the current to decay to e-1 » 37% of its original value.  By inspection, Eq. 3 predicts that t  = L / R  (tau=L/R.)

An oscilloscope is a voltmeter rather than an ammeter, so we cannot measure the current in the circuit directly. But we do know that the voltage across the resistor is just V = IR, so when the current drops to 37% of its original value, the voltage across the resistor drops to 37% of its original value as well. Marks on the oscilloscope help you determine precisely where the voltage drops to 37% of its original value. Use the oscilloscope knob that tells you the time per division to determine the time it takes for this to happen. Note that one division is distance between solid vertical lines. Small tick marks on the screen can help you make a more accurate measurement of the time.

Using two different values of the load resistance, measure t (tau) on the oscilloscope and compare to the calculated L/R value.  Note: do not neglect the small internal resistance of the inductor in your calculations.

   R+Rinductor: Ohms     L:  H    Calculated t (tau):  s    Measured t (tau): s

   R+Rinductor: Ohms     L:  H    Calculated t (tau):  s    Measured t (tau): s