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Faraday’s Law and Inductors
Equipment Needed Part I
AC/DC Electronics Laboratory,
Pasco EM-8656
Coil, Pasco (400) SF-8610
Galvanometer, Cenco (analog)
Lead, Banana w/ clips
Magnet, Cow
Power Supply, Fisher-EMD S44175-1
Battery Eliminator
Resistance Decade Box, TENMA 727270
String, Black
Equipment Needed Part II
AC/DC Electronics Laboratory,
Pasco EM-8656
Cable, BNC Banana
Cable, BNC/Alligator
Function generator, 10Mhz BK
Precision 4017A
Inductor 1mH (½Ω)
or
Cable, Passive BNC/Probe (2)
Oscilloscope, Tektronix TDS 1002B
Capacitor, 10  F
Resistor, 100Ω
Capacitor, 0.1 F
Introduction
Inductors and capacitors are the primary “passive” energy storage devices in
electronics. When inductors and capacitors are wired together a resonant circuit
is formed that is very useful in tuning in signals in devices such as radio and TV
receivers. A time-varying current passing through an inductor produces a backEMF across the coil that can be measured. As a preliminary step we will first
examine the minus sign in Faraday’s law, also known as Lenz’s law, with the aid
of a bar magnet and a galvanometer.
Part I
Procedure
1. Wire the battery eliminator through the Resistance Substitution Apparatus (RSA)
and to the galvanometer as shown in Figure 1 (next page.) Set the RSA on
100k . Set the Battery Eliminator to 6vdc. Caution: Double check your
settings to make sure you don’t blow out the galvanometer. Turn on the
power supply and verify which terminal current must flow into for the
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galvanometer to display a needle deflection to the right. Many of the
galvanometers have been labeled by hand showing which terminal is plus.
However, the galvanometer may have been labeled incorrectly. Your job is to
check this labeling.
Figure 1 Schematic and Physical Layout of Circuit to determine galvanometer polarity
DC
Galvanometer
Resistance
Decade
Box
2. Record which terminal (right or left)
causes a rightward needle deflection.
Figure 2 Cow Magnet
Suspended
3. Suspend the cow magnet with the black
string as shown in Figure 2 and determine
which end of the magnet is the north pole
and north seeking pole.
4. Connect the induction coil (400 turn)
directly to the galvanometer such that if
current is flowing clockwise in the coil a
rightward needle deflection occurs. The arrow on the coil indicates the direction
of the winding.
5. Push the north end of the cow magnet into the coil as shown in Figure 3 on the
next page. When the magnitude of the flux is increasing which way does the
needle deflect (right or left)? Which way was current induced in the winding
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(clockwise or counter clockwise)?
Figure 3
When the magnitude of the flux is
decreasing which way does the needle
deflect? Which way was the current
induced in the winding?
6. Push the south end of the cow magnet
into the coil. When the magnitude of
the flux is increasing which way does
the needle deflect? Which way was
current induced in the winding? When the magnitude of the flux is decreasing
which way does the needle deflect? Which way was the current induced in the
winding?
Results Part 1
1. Are your results consistent with Faraday’s law?
2. Are they consistent with Faraday’s law for all four cases?
a. Flux into the coil and increasing
b. Flux into the coil and decreasing
c. Flux out of the coil but increasing in magnitude
d. Flux out of the coil but decreasing in magnitude
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Part II
Procedure Part IIA
1. Build the circuit shown in Figure 4 with the Pasco electronics laboratory. Your
goal is to view the voltage across the function generator on the oscilloscope’s
channel 1 and the voltage across the resistor on the oscilloscope’s channel 2. The
oscilloscope has a great many knobs and settings so please have your instructor
check your oscilloscope settings for you. The channels should be DC coupled and
the trigger should be set to automatic. The channels may be viewed
simultaneously in either alternate or chop mode. Make sure the invert switch is
off and the vertical sensitivity fine vernier and time sweep fine vernier are in the
locked position.
Figure 4: Circuit to measure AC steady state response of inductor and resistor in series.
Pasco Laboratory
1 mH
A
B
100 Ω
C
Attach Channel 1 probe to A
Attach Channel 2 probe to B
Ground for generator and
both Probes is C
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2. Set the function generator to 1kHz with a 1 volt peak output. Record the
amplitude of the voltage across the resistor. Record the phase shift (if any)
between the two oscilloscope channels. Write down which waveform “leads” and
which waveform “lags.” The wave form with peak occurring at earlier time is
said to lead. Note that the measured phase shift in radians can be found from
Phaseshift 
d peaks
d cycle
 2
Equation 1
where
d peaks  number of divisions between peaks of the two signals
d cycle  number of divisions for one cycle
3. Repeat Step 2 for 5 kHz, 25 kHz, and 125 kHz.
Calculations and Results for Part IIA
For each frequency tested answer the following:
1. What is the value of the peak current flowing in the circuit? What is the value of
the RMS current flowing in the circuit?
2. What is the value of the inductive reactance at this frequency? What peak voltage
ought to be across the inductor? What RMS voltage ought to be across the
inductor?
3. Use the phasor diagram (Figure 5) below to derive the theoretical relationship
between the voltage across the resistor and the voltage across the function
generator. Note that in the diagram the voltage across the resistor and the current
through the resistor are assumed proportional to cos t  as discussed in class.
Also find the theoretical relationship between the phase of the voltage across the
resistor and the voltage across the function generator.
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Figure 5 Phasor diagram for LR circuit
4. Compare the theoretical and experimental values for the ratio of the peak voltage
across the inductor to the peak voltage across the resistor. Compare the
theoretical and experimental values for the phase shift between these two
voltages. Which voltage leads?
Procedure Part IIB
1. Modify the circuit on the Pasco Lab board to include a series capacitor as shown
in Figure 6. Use the 0.01 F capacitor if it is available. Otherwise use a 10  F
electrolytic capacitor.
Figure 6 Circuit diagram for LCR circuit
Pasco Laboratory
1 mH
A
C
Attach Channel 1
probe to A
Attach Channel 2
B
probe to B
100 Ω Ground for generator and
both Probes is C
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2. Compute the resonant frequency of the inductor and the capacitor from the
formula:
1
LC
res 
Equation 5
3. Compute the Q of the circuit from the formula:
Q
 res L
R
Equation 6
4. Measure the ratio of the voltage across the resistor to the voltage across the
function generator for several frequencies around resonance.
Calculations and Results Part IIB
Plot your results to Part IIB item 4 above. In particular plot the square of the
voltage ratio vs. frequency. If the Q value is larger than 2 or 3 you should find
Q
 res

Equation 7
as discussed in your text. Does your plot indicate a Q value in agreement with the
theoretical prediction?
Conclusions
Summarize your findings. Do the theoretical and experimental results agree?
What percent error did you observe? Has the resistance of the coil had a big
impact on the results? Why do you think this is the case?
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