Name______________________
Date__________ Period_______
To gain an understanding of inductors and its properties through the observation of data collected from a simple RL circuit, set up by measurements of its voltages and currents through the inductor and resistors.
The RL Circuit describes a circuit that consists of a resistor(s), a inductor(s), and a voltage input into the circuit.
The RL Circuit will be set up as the following, where two separate voltmeters will measure the output voltage across both the inductor and the resistor at the same time. Using
PASCO Capstone software, the changing voltage and the resulting rate of change of the voltage across the resistor and inductor will be shown. From the recorded data, students can calculate for the time constant of RL circuits as well as fundamentally observe the effects of an inductor.
● PASCO RLC Circuit Board
● (2) Voltage Sensor (CI-6503)
● (2) banana plug patch cords (ex. SE-9750)
● PASCO 850 Universal Interface (built in power amplifier)
● Pre made PASCO Capstone file (LRCircuits.cap file)
1. Connect ends of the two voltage sensors into channels A and B of the interface.
2. The ends of the voltmeter stemming from Channel A will represent the voltage output across the inductor for the purposes of this lab. Hence, connect the alligator clips of Voltage Sensor A across both sides of the inductor coil that is built into the given circuit board.
3. Do the same for the other voltmeter, except that it will be across the 10 ohm
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resistor. Voltage Sensor B will represent the voltage output across the resistor.
4. Remaining banana plug patch cords should be connected from the output of the built in power amplifier that is located on the very right of the universal interface.
Both plugs should be connected to the banana jacks as shown in the following, that will act as the driving voltage source.
5. Open the given file labeled “LRcircuit.cap.” Ensure under signal generator that the current being driven through the circuit is in the form of an AC square wave. a. The AC square wave will have no effect on the given circuit - it will rather just act as a turning on and off direct current. b. *All other conditions including frequency, current source, voltage source, starting/ending conditions will be automatically set up for the purposes of the lab. Calibrations are not necessary, and the graphs given will record measurements of voltage.
6. Ensure that the PASCO Capstone is readily hooked up to the circuit by clicking on the left side “Hardware Set Up.” If there is no green colored confirmation that the voltmeters are being read by the software, click on the visual representation of the interface where the actual voltmeters go, scroll, and select “voltage sensor.”
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1. Derive the expressions for voltage across an inductor and the resistor once a DC voltage is applied to the RL circuit below.
V
R
V
V
=
L
L
= L ( di / dt )
= V o
V o e −( t / τ )
( 1 − e −( t / τ ) )
2. Sketch below the expected graph of both the voltage across the inductor and resistor below based on the derived equations.
3. The lab should now be ready to run. Once ready, click on the record button (red circle near the bottom of the screen) to record data.
4. All graphs should be labeled by a given key on the screen itself.
*TEACHER NOTES ONLY: The changes in voltage occur instantaneously (usually less than a quarter of a second). Therefore, in order to properly observe the gradual change of output voltage in the circuit, properly adjust the axis of the graph so that the time value on the x axis is decreased, and the graph overall somewhat looks like this:
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Part I Calculating a range for the inductor’s internal resistance.
= L / ΣR, where L is given by 8.2 mH = 0.0082 H, and
R is the total resistance of the circuit that includes both the resistance of the resistor and the resistance of the coil.
Hence, the R value here would be (10 + Ri).
The definition of t
1 / 2
is the time for the current to rise or fall (and thus the voltage across the resistor, since they’re in phase with each other) to half it maximum. It is equal is equivalent to
(ln 2).
t
1 / 2
I = I o
= τ ( ln 2 ) *
This equation can be derived from:
( 1 − e −( t / τ )
)
Derive in the following space:
*See derivations attached on bottom; TEACHERS NOTES ONLY
The experimental value of t
1 / 2
presents a challenge, however, as the graphs are not the ideal perfect circuit as given in CollegeBoard problems. The following are given sample graphs the student should be seeing:
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Estimate the time where V = 0. This will be the reference point you will be using as this is when the voltage is applied to the circuit; in the example, the reference time is .015s.
Take the time difference between this reference point and the point where voltage reaches its half-peak. This will be your experimental value of t
1 / 2
; in the example, it reaches the half-peak at .0155s, so t
1 / 2
= .
0005s
The final value of ( t
1 / 2
) will have an error bound, due to the imperfect circuit leading to a non ideal graph of the voltage graph. The error bound is
𝟎 .
𝟎𝟎𝟎𝟎𝟎. With this error bound in mind, compute a range for possible values of the internal resistance.
R
L
= L /( t
1 / 2
) − R r
Part II. Confirming the internal resistance of the inductor
Calculate the internal resistance of the inductor using the following equations.
𝟎 = 𝟎 / 𝟎𝟎
𝟎
𝟎
𝟎 = 𝟎
𝟎
𝟎 = 𝟎
𝟎
/ 𝟎
𝟎
=
/
/
𝟎
𝟎
𝟎
𝟎
𝟎
𝟎
/ 𝟎
𝟎
Solve for the value of 𝟎
𝟎
. Confirm that this value falls under your range from Part I.
R and V
L
are calculated values from the graph at 4V and 2V Given R
R
= 10Ω, and V respectively, the resistance that the inductor provides can be given. Value should = 5
Ω
R
L
(Part I Range)
𝟎
𝟎
(Actual, Part II)
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1. Why does the voltage across the inductor not decrease to 0 as it may be expected theoretically?
2. If the circuit was turned on long enough for constant values of current to be reached, and then all of a sudden the voltage source was cut off, how would the graphs measuring the values of voltage across the inductor and resistor differ
3. Add the iron core given with the circuit into the coil of the inductor. Run the same experiment again. Is there any difference to the given values, such as the value of the inductor? Explain why or why not.
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