ElectronicsLab5.nb
Often you deal with a complicated electronic circuit. It is often the case that the behavior of one particular component is crucial. For example, you could have an stereo amplifier connected to a speaker.
You would NOT be particularly interested in how the amplifier works in detail and you would only be interested in how the amplifier interacts with the speaker. For your purposes, the amplifier is a "black box" that produces some effect at the output terminals and the speaker is connected across the output terminals. A diagram of the situation appears
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The speaker serves to convert electrical energy into acoustic energy with an electromagnet near a metallic diaphragm but for our purposes it is simply a resistance R output
. Thevenin's theorem says we can replace the entire amplifier by an effective or equivalent battery (or voltage source) V
EQ
in series with and effective or equivalent resistance R
EQ
. Thus the above diagram appears according to Thevenin's theorem where the equivalent resistance R
EQ and equivalent battery V
EQ of the amplifier are in series with the output resistance R
OUT
. The claim is that any complicated circuit having resistors and batteries can be represented by a Thevenin equivalent circuit like that drawn above. We do NOT prove the theorem here
(this is a subject in an electrical engineering course) and we simply show it is true for an example.

ElectronicsLab5.nb
where the equivalent resistance R
EQ and equivalent battery V
EQ of the amplifier are in series with the output resistance R
OUT
. The claim is that any complicated circuit having resistors and batteries can be represented by a Thevenin equivalent circuit like that drawn above. We do NOT prove the theorem here
(this is a subject in an electrical engineering course) and we simply show it is true for an example.
2
A previous lab lecture solved the circuit below using conventional methods. The circuit has three resistors: R
1
and R
2
are in parallel while R
3 is in series with the parallel combination.
Suppose the same two resistors as before, R
1
= 30, 000 W and R
2
= 50, 000 W are in parallel, and this combination is in series with R
3
= 20, 000 W The battery voltage is V-12 Volts as before. In a previous la using simple reduction methods we obtained the current through R
2 as i
2
=0.12 ma. Here we show that
Thevenin's theorem gives the same result for the current as an illustration of Thevenin's theorem. Since we are focusing only on the current through the resistor R
2
we relabel it the output resistance R
OUT
.

ElectronicsLab5.nb
Thevenin's theorem claims the above circuit can be replaced by an equivalent or effective circuit indicated below:
Notice the equivalent voltage V
EQ
is NOT the original battery voltage and the equivalent resistance R
EQ is NOT simply R
1
or R
2
or R
3
. We now give Thevenin's prescription for calculating R
EQ
and V
EQ
.
EQ
Thevenin's theorem says you calculate the effective or equivalent resistance R
EQ
by (1) removing the battery from the ORIGINAL circuit and (2) replacing the battery by a short circuit wire. Also, the (3) output resistance R
2 is removed from the circuit. The resistance measured at the output terminals is R
EQ operationally (experimentally) and theoretically. The original circuit appears after the above operations
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ElectronicsLab5.nb
The above circuit is equal to the circuit below of two resistors in parallel:
At first, you might not believe these two circuits are equal electrically. To convince yourself of this fact make sure to understand that the connections of the two resistors to terminal A are the same in both circuits and the connections to terminal B are the same in both circuits.
The equivalent resistance is the of two resistors in parallel, that is
1
R
EQ
=
1
R
1
1
+
R
3
Numerically this is for the case at hand
(1)
1
R
EQ
=
1
30, 000 W
+
1
20, 000 W and Mathematica yields
(2)
4

ElectronicsLab5.nb
1
30 000
+
1
20 000.
0.0000833333
and further taking the reciprocal
1
R
EQ
=
0.000083
12 048.2
Thus the equivalent resistance for this circuit is R
EQ
=12 k W .
EQ
Thevenin's theorem says you calculate the effective or equivalent voltage V
EQ
by (1) returning the battery from the ORIGINAL circuit and (2) removing the output resistor R
OUT
=R
2
. The equivalent battery V
EQ
is the voltage measured or calculated at the output terminal as indicated below:
5
Resistors R
1 and R
3
are in series and the voltage is measured across R
1
. The above circuit is effectively a voltage divider so the equivalent or effective voltage V
EQ
is
R
1
V
EQ
=
R
1
+ R
3
V
For the case at hand, the numerical value of V
EQ
is
(3)
V
EQ
=
30, 000 W
30, 000 W + 20, 000 W
12 Volts (4)

ElectronicsLab5.nb
Mathematica yields
V
EQ
=
30 000
30 000 + 20 000.
12
7.2
so V
EQ
=7.2 Volts.
The Thevenin equivalent circuit for this problem with the numerical values used appears
6
It is now an easy matter to calculate the current through the output resistor and one obtains via Ohm's law i =
V
EQ
R
EQ
+ R
OUT
7.2 V
=
12, 000 W + 50, 000 W
Mathematica yields
(5)
7.2
12 000 + 50 000
0.000116129
Thus using the Thevenin's theorem we obtain the output current i=0.12 ma which is the same number as obtained using the simple series and parallel circuit analysis. This example should give you more confidence in the Thevenin theorem; however, you should work other examples and show that the simple direct method and Thevenin's theorem both give the same answers. Thevenin's theorem is a powerful and useful means of dealing with complex circuits if you want to focus on the behavior of one circuit element.

ElectronicsLab5.nb
Series and Parallel Resistors Circuit : Pick three resistors from your parts box in the 10,000 W range. (It would be helpful if these were the same three resistors you used in the last laboratory.) Measure the resistances using the Ohmmeter and make sure the values agree with the color code. Connect the resistors in series and parallel as indicated in the above discussion. Measure the equivalent resistance using
Thevenin's procedure and see that this resistance agrees with what you expect from numerical calculation.
Measure the equivalent voltage using Thevenin's procedure and see that this voltage agrees with what you expect from numerical calculation. Finally use Ohm's law to calculate the current through the output resistor and see that this current agrees with the value of the current measured with an ammeter. You can also measure and calculate the output voltage across the output resistor.
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