Lab #4 Thevenin’s Theorem

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Oct 10, 2013 (3 years and 10 months ago)

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ECE 170 Lab
#4 Thevenin’s Theorem

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-
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Lab #4 Thevenin’s Theorem



In this experiment you will become familiar with one of the most important theorems in
circuit analysis, Thevenin’s Theorem.


Thevenin’s Theorem can be used for two purposes:


1.

To calculate the current through (or voltage acros
s) a component in any circuit,


or


2.

To develop a constant voltage equivalent circuit which may be used to simplify
the analysis of a complex circuit.


Any linear one
-
port network can be “replaced with” a
single voltage source in series
with a single resis
tor (see Figure 1 below).
The voltage source is called the Thevenin
equivalent voltage, and the resistor is called the Thevenin equivalent resistance. What
this means is that a single voltage source and series resistor will behave identically to
the actua
l part of the circuit it is replacing.


In this experiment, you will use Thevenin’s theorem to solve a complex DC circuit.

















Figure 1 A network replaced with its Thevenin equivalent circuit


ECE 170 Lab
#4 Thevenin’s Theorem

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The steps us
ed for Thevenin’s Theorem are listed below
:


Step 1

Remove the resistor (R) through which you wish to calculate the current or across which
you want to know the voltage. Label these terminals (where the resistor was removed)
“a” and “b”. Calculate the vo
ltage across these open terminals. This is called the open
circuit voltage or the Thevenin equivalent voltage,
V
TH
.





Step 2

From the open terminals, (“a” and “b”) calculate the resistance “
looking back
” from the
open terminals with
all voltage sources removed and replaced by their internal
resistances (if R
I
nternal

= 0, replace the voltage source with a
short
). This resistance is
R
TH
.







Now we have the components we need to create the Thevenin equival
ent circuit as
shown below

using the Thevenin equivalent voltage and resistance values calculated
above connected in series with the load resistor as shown below.







+

V
TH




R
TH

ECE 170 Lab
#4 Thevenin’s Theorem

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Step 3

The current (through R) you wish to calculate will be:





and the voltage across R will be:




where:
V
TH

is from Thevenin equivalent voltage obtained in Step 1,
R
TH

is the Thevenin
equivalent voltage obtained in S
tep 2, and
R

is the value of the resistor removed in Step
1.



Instructional Objectives


4.1) To work through the procedural steps involved in Thevenin’s theorem.

4.2) To verify the values obtained by measuring them using the digital multimeter.

4.3) To co
nstruct a Thevenin equivalent circuit.



Procedure


a) Connect the circuit in Figure 2. We will use Thevenin’s theorem to find the current
through R3.


Figure 2


b) Measure the current through R3 and the voltage across R3. Record them:


I
R3
= _________
_________(meas) V
R3
= ___________________(meas)


c) You will now use Thevenin’s Theorem to calculate the current through R3, by
following the steps outlined in the introduction.
SHOW ALL WORK in the space
provided
. Record the results for each step in th
e space provided.

ECE 170 Lab
#4 Thevenin’s Theorem

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Referring to Figure 3, which is Figure 2 with R3 removed, calculate V
TH

in Figure 3,
showing all work.



Figure 3
























V
TH
= ________________________(calc)




d) Verify the actual Thevenin equivalent voltage by measure
ment: Construct the circuit in
Figure 3, and measure and record V
TH
.



V
TH
= ____________________________(meas)



ECE 170 Lab
#4 Thevenin’s Theorem

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e) Construct the circuit in Figure 4, which is the circuit in Figure 2 with R3 removed and
the 12 V source replaced by a short circuit (a dea
d voltage source). Calculate R
TH

in
Figure 4,
showing all work.


Figure 4


















R
TH

= _________________________(calc)


f) Verify your R
TH

calculation by measurement. Connect Figure 4, and measure and
record the equivalent resistance (R
TH
) meas
ured between terminals a and b.


R
TH

= _________________________(meas)


g) Draw below the Thevenin equivalent circuit, using your calculated values for V
TH

and
R
TH
.
This diagram is Figure 5.












ECE 170 Lab
#4 Thevenin’s Theorem

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h) Calculate I
R3
using the Thevenin equivalent circ
uit (the V
TH

and R
TH

you found
above).




i) Compare the current measured in step 1b (original circuit) and the current calculated in
step 3 above (which used Thevenin’s Theorem). If they are not reasonably close, find
the reason for

the discrepancy).


j) Build the circuit of Figure 5. Obtain a resistor for R
TH

as close as possible to its
calculated value (or use a potentiometer or a decade box, whose value you can set
equal to R
TH
)
.


k) Measure the current through R3 and the voltage
across R3 in the circuit of Figure 5.
Record them:


I
R3
= _____________________(meas) V
R3
= ____________________(meas)


l) Compare these measured results with the results of part b (the original circuit). If the
results are not close, find the reason for t
he discrepancy.





Post Lab Questions


1.

What is meant by the word "equivalent" in Thevenin Equivalent circuits?


2.

What is the practical value of Thevenin Equivalent circuits? Give several
practical applications in which Thevenin Equivalent circuits are use
d.


3.

For the following circuit, use Thevenin’s theorem to find the current through R.

Show the Thevenin equivalent circuit you used and the values of R
th

and V
th

you
obtained.


ECE 170 Lab
#4 Thevenin’s Theorem

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7

Name:

____________________



Section:

____________________


Pre
-
Lab #5: Digit
al Oscilloscope



Figure 5.0: Oscilloscope Screen for Problem 1.


1.

The oscilloscope screen displayed in Figure 5.0 has the following properties:



V/div setting = 1V/div



S/div setting = 1mS/div

a)

What is the frequency of the si
gnal?



b)

What is the trigger level setting on the oscilloscope?



c)

What is the slope setting on the oscilloscope?



d)

Recalling trigonometry, the equation of a wave of this nature is given as

v(t) = V
max

sin(

t) + V
dc
.

Therefore, what is the equation of the ab
ove wave?





2.

What does a 10:1 oscilloscope probe do?