Understanding RL Circuits (Lab 9)

Goals:
RL Circuits
To quantify the rate at which the potential difference across an inductor changes when
connected in series with a resistive element.
To discuss differences in the behaviors of a circuit with only a resistive element, a circuit
with a capacitor in series with a resistive element, and a circuit with an inductor and a
resistive element.
To practice linearization of data as a data-analysis technique.
Equipment:
Science Workshop Interface
Voltage Probes
Digital Multimeter (DMM)
Phys212 LabKit Module
RLC circuit board
5 and Diode Circuit board
High inductance coil
(7) Stackable banana-plug connecting wires
(4) Alligator connecting wires
Software: Microsoft Excel, DataStudio
Introduction:
In an earlier lab, we examined how capacitors and resistors interact in a circuit. In this lab, we
will study how indutors and resistors interact in a circuit (called an RL Circuit). We will
approach this qualitatively and then quantitatively.
Due to Faraday’s Law, inductors oppose changes in the current through them. Any change in
current changes the magnetic field created by the inductor which means that the magnetic flux
through the inductor changes. This change in flux induces an EMF to oppose the change. The
induced EMF, induced , of an inductor is given by:
di
induced
L
(Eq. 1)
dt
di
where L is inductance, and i is the current through the inductor (so is the rate of change of the
dt
current). The negative sign comes from the fact that this induced EMF creates a magnetic field
which opposes the change in flux. A capacitor’s capacitance depends how it was made (i.e. size
/ shape of the terminals, how they are separated, what material is between them), and a resistor’s
resistance depends how it was made (i.e. what material it was made of and what shape it is). The
inductance of an inductor is given by:
B
N L B-one
(Eq. 2)
i i

PHYS 212 Lab Understanding RL Circuits 2
where B is the magnetic flux through the inductor. This magnetic flux is the flux created
through the inductor by the current which passes through it (this is why inductance is more
properly called “self-inductance”). The inductors we encounter are often made of many turns of
wire and so it can be useful to note that the magnetic flux could be looked at as the magnetic flux
created by one turn of wire ( B-one ) multiplied by the number of turns of wire (N) making the
inductor. In other words, the more turns of wire an inductor has, the larger its inductance will be.
The inductance can also be increased by placing a ferromagnetic material within the center of the
inductor. The magnetic field created by the inductor in the current will magnetize this core; as
the inductor’s magnetic field changes so will the magnetization of the core. This in turn will
correspond to a larger change in flux.
When an inductor is connected in series with a resistor of resistance R and a power supply or
battery with EMF , the inductor will oppose any change in flux (by trying to keep the current at
its initial value, zero). This will cause the voltage across the inductor to spike. The voltage
across the inductor then decays with time. As the inductor opposes the change in current, the
current will increase rapidly at first, then the rate at which the current changes will decrease as it
eventually reaches a final steady-state value. This process is described by the equations
t
i t 1 e
(Eq. 3)
R
and
V
L
t
t
e
(Eq. 4)
As with an RC circuit, the quantity t is called the time constant of the circuit. For an RL circuit,
the time constant is given by
L
(Eq. 5)
R
If an inductor has a current through it and then is removed from the battery in such a way that it
is still connected to a resistance R, the inductor will still oppose any change in flux (by trying to
keep the current at its initial value and direction, whatever those are). The current through the
inductor will decrease rapidly but then the rate will slow as it approaches zero. This process is
described by the equations
t
it
e
(Eq. 4)
R
and
V
L
t
t
e
(Eq. 5)

PHYS 212 Lab Understanding RL Circuits 3
Name: ____________________________
Name: ____________________________
Name: ____________________________
Date: ______________
Lab Sect.: __________
Lab Instructor: ______________________
Directions:
Lab Activity 1: Charging and Discharging of RL Circuit
Construct the circuit shown in Figure 1 below. Make sure that you connect the batteries
to each other with the correct polarities (i.e., the positive end of one battery connected to
the negative terminal of the second battery). The resistor in the circuit is the round bulb
on the same circuit board as the switch. The switch has two possible closed positions,
labeled A and C. Position A requires the switch to be held to keep it closed. Because we
do not want to accidentally leave the batteries connected to the circuit, in this lab, we will
only use position A. Also make sure that the light bulbs are properly screwed into their
sockets.
A
B
C
Figure 1 A circuit with two batteries and a light bulb. Please ask your teaching assistants if you
are unsure about your wiring of the circuit.
Throw the switch to A for a few moments and observe the light bulb. Throughout this
lab, wait at least thirty seconds between runs to ensure that the light bulb cools.
Q1. What happens to the light bulb when the switch is thrown to A (this is not a trick question,
just describe what happens)?
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PHYS 212 Lab Understanding RL Circuits 4
Q2. What happened to the light bulb in an RC circuit (look back at “Understanding RC Circuits”
if you can’t recall)?
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.
Open DataStudio (start → Programs → DataStudio → DataStudio), and click on
Create Experiment.
Click on Add Sensor or Instrument.
Select Voltage Sensor
Click and drag the Graph icon onto the Voltage Sensor icon.
Click and drag the Table icon shown above to Voltage Sensor icon.
You should feel free to arrange the displays as you see fit. After doing this, your screen
should display the Graph and Table display.
Change the sample rate for the Voltage Sensor from 10 Hz to at least 4,000 Hz. The
changes we will record have a very short time scale; the Science Workshop 750 Interface
has a maximum sample rate of 250,000 Hz when using a single analog sensor.
Modify the circuit to be the one shown in Figure 2 below. One of the two inductors, is on
the “RLC Circuit” board and the other is the “High Inductance Coil” attached to the
wooden board. Some things to keep in mind while you are constructing this circuit:
o The RLC Circuit board has wires embedded in it (the white lines show where they
are). To connect the inductor (the spool of wire), insert one banana plug wire into
the socket on either side of the inductor. Remove the metal bar from the RLC
Circuit board and insert it into the center of the inductor. This will increase its
inductance.
o To ensure a good connection for the High inductance coil, connect an alligator
clip to both of the two brass posts sticking out of the wooden board. Connect the
other ends of the alligator clips’ wires to banana plugs to be used with the circuit
boards.
o Do NOT close the circuit yet (i.e., leave the switch in the open position B).

PHYS 212 Lab Understanding RL Circuits 5
A
B
C
Figure 2 An RL charging circuit. Please ask your teaching assistants if you are unsure about your wiring of the
circuit.
Q3. Why have we asked you to connect the two inductors in series like this? Things to consider
to help answer this: What should connecting the inductors in series do to the total inductance
and why (with physical reasoning, not just quoting an equation)? Why might we want to make
that effect to the total inductance (look back at the RL circuit equations)?
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PHYS 212 Lab Understanding RL Circuits 6
Q4. Predict what will happen to the voltage across the inductors after you close the switch to A
and then release the switch. Sketch (qualitatively) below what you expect the time variation of
the voltage to look like including what should happen after the switch is released. Label the point
at which you would release the switch from A. (Alternatively, you can make a graph using Excel
and attach it to your lab report, if you so wish.) Explain why you drew those forms.
DV L
t
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PHYS 212 Lab Understanding RL Circuits 7
Q5. Now, actually throw the switch to A for a few moments and observe the light bulb.
Describe (qualitatively) what happens to the light bulb when you move the switch to position A
(including any differences between this circuit and the one with only a light bulb or an RC
circuit).
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Connect the voltage probes to measure the voltage V L across the inductors.
Click on the Start button in DataStudio to begin recording data, and close the circuit by
moving the switch to position A.
o When a steady state has been reach, release the switch
o When a new steady state has been reached, stop recording data by clicking the
Stop button in DataStudio.
You might wish to do this a few times in order to get a reasonable set of data. Note that
you can delete any set of data simply by highlighting the name of the data set in the Data
window and then pressing the Delete key.

PHYS 212 Lab Understanding RL Circuits 8
Q6. Sketch (qualitatively) the time variation of the measured voltage across the inductors. Label
the point at which you released the switch from A. (Alternatively, you can print the graph and
attach it to your lab report, if you so wish.) Make sure your graph includes what happened after
the switch was released. If some parts of the behavior, have different time scales than others,
you should include multiple graphs (one for each section of the behavior).
DV L
t
Q7. Discuss any differences between your graph from Data Studio (Q6) and your initial sketch
(Q4). What might have caused them (explain at least one difference between the two graphs; if
there are no differences, then be sure you completely explained all of the features you predicted
above in Q4)?
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PHYS 212 Lab Understanding RL Circuits 9
Q8. As a reminder, here is what the voltage across a charging and then discharging capacitor
looked like (from the lab “Understanding RC Circuits”):
DV C
Start Discharging
t
Qualitatively compare and contrast this and what you observed for the inductor. Explain any
differences or similarities. (Hint: Since the inductor opposes changes in current, when it is first
connected, what does it act like? When it is connected for a long time, what does it act like?)
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Move the voltage probes so that you are measuring the voltage across the light bulb, V R .

PHYS 212 Lab Understanding RL Circuits 10
Q10. Attach the graph of measured voltage across the bulb V R vs. t to your lab report. Label the
point at which you released the switch from A.
Q11. Explain qualitatively why the voltage across the bulb varies as observed. Explain what that
means about the current through the light bulb and so your observations in Q5.
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PHYS 212 Lab Understanding RL Circuits 11
Lab Activity 2: Quantitative Analysis of an RL Circuit
In this activity, we’re going to distinguish between V L-total (the total voltage across the inductors
at any time), V L (the voltage across the inductors due to their inductance and a changing current),
and V L - R (the voltage across the inductors due to their resistance). The three are related by:
V L-total = V L + V L-R (Eq. 6)
Modify (re-wire) your circuit so that the 5 resistor on the separate circuit board is used
in place of the light bulb. (Since the resistor is ohmic, we won’t have to worry about any
non-ohmic behavior of the light bulb.)
Repeat the first experiment that you carried out earlier: i.e., record the voltage V L-total
across the inductor as a function of time after you have placed the switch at A
Export the measured data to an Excel spreadsheet for analysis as follows:
o In the Table display, highlight the columns of data containing the time and
voltage readings.
o Copy this to the clipboard (Press Ctrl-C or select Copy from the Edit menu)
o Open Microsoft Excel and start a new spreadsheet.
o Paste (Ctrl-V) the copied data into the first two columns.
o Check the units on the data columns so you can label your graphs properly
Q12. Use Excel to make a graph of V L-total versus t from the point after you moved the switch to
A to just before you released the switch. Remember to label the axes on your graphs correctly
with proper units. Include this graph with your lab report.
Q13. If we rescale the data to remove the steady state voltage (V L-R ), we’ll be able to find the
time constant fairly easily (this is making the approximation that the voltage change due to the
inductors’ resistance is constant which isn’t quite right). Rescale the data and use Excel to make
a graph of V L versus t just between the point when you moved the switch to A and when the
steady state was reached. Remember to label the axes on your graphs correctly with proper
units. Include this graph with your lab report.

PHYS 212 Lab Understanding RL Circuits 12
Q14. How would you plot the data in such a way that tests whether it obeys the RL circuit
equations? (Note that the easiest type of data to fit is a straight line! So, think about how to
transform the equation into a form that allows you to see whether the data follows a straight line.
Think logarithms! You may need to make new columns in your Excel file) Include this plot with
your report. From the plot, determine the value of the time constant. Explain below how you did
this and include any comments that you can about the size of the time constant. (Include your
new graph.)
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