Experiment 9
The RL Series Circuit
The voltage as a function of time across an inductor in an RL series circuit is observed on an oscilloscope and compared to the theoretically calculated plot when the parameters of the circuit are known.
Theory
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When a square wave generator is connected to an inductor and resistor in series, the circuit looks as shown in Figure 1. The inductor in the circuit has an inductance L and resistance RL, the generator has an output resistanceRG,and the additional resistance from a resistance box is R.
The square wave generator acts like a battery switching into the circuit with a voltage 6 then shorting out periodically. If it is switched into the circuit at time t = 0, then the current flow at any time t is
Figure 1. The RL series circuit.
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(1)
where RT=RG+RL+ R. The voltage across the inductor is then
(2)
where VL is the voltage due to the inductance part of the inductor and VRis the voltage due to the
resistance of the inductor. You now are to derive an expression for the voltage across the induc-
as a function of , RL, RG, R and T. This equation is to be graphed against time.
Apparatus
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o inductor, approximately 20 mH
o oscilloscope with leads
o 1 sheet of graph paper
o decade resistance box
o 3 leads
o signal generator
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Procedure
1)Connect the circuit as shown in Figure 1. Be sure that the signal. generator is in the square wave mode.
2)Adjust the resistance box until the total resistance of the circuit is 500 ohms, i.e., RT=RL+ RG+ R = 500.
3)Use the value of 800 mv as and substitute this value together with the parameters of your circuit into the equation you derived for the voltage across the inductor. Calculate numerical values for the voltage across the inductor at time t = 0, t = L/R, t = 2(L/R), t= 3(L/R), t = 4(L/R), and t = 5(L/R). Graph these values on a voltage versus time graph filling as much of the page as possible. Label this graph as the theoretical graph. Before continuing, show the graph to the instructor for approval.
4)Once approval has been obtained, tum on the equipment and adjust the signal generator and the oscilloscope until the trace appears as shown in I Figure 2. Be sure that the horizontal sweep knob on the scope is in the calibrate position.
Figure 2. The initial adjustment of the oscilloscope trace.
5)Now adjust the, . vertical sensitivity until the 0 volt reference line (as shown in Figure 2) lines up with the bottom graticule on the oscilloscope screen. Set the VOLT/DIV knob at 100 mv/div and adjust the amplitude of the peak to 8 divisions. The signal now has an initial voltage of 800 mv.
6)Now adjust the sweep speed on the oscilloscope (also the horizontal. magnification, if necessary) until only the first half of the trace shown in Figure 2 fills the screen. The horizontal adjustments, except for calibration, can be changed at will; however, do not change the vertical settings.
7)Record the voltage values from the oscilloscope for times of one, two, three, four, and five time constants. Plot these as the experimental points on your graph of voltage versus time. Be sure to distinguish them from the theoretical points.
Analysis
The graph shows the relationship between the theoretical and experimental values of the
voltage across an inductor that has resistance.
An optional exercise is to perform the above procedures for the voltage across the
resistor.
Questions
- Derive (1), then use (1) and (2) to derive the expression for the voltage across the inductor in terms of 6, L, RL,RG,R, and t.
- Suppose that the voltage F, is connected for a long time and steady state is reached. If the voltage F, is now shorted (i.e., = 0) at time t = 0, then derive an expression for the current in the circuit at some later time t in terms of , L RL, RG, R, and t.
- What is the reason for the gap that exists between the two flattened portions of the curves shown in Figure 2?
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