Getting Started with EasyCircuit
Open a chrome browser (or your
android tablet or if you have to a ipad)
and navigate to everycircuit.com.
Create a new account for your group
by choosing sign in. Note only one
account per lab group! Make sure
everyone in the group knows the
password to the account.
Once you have created the account,
select Profile and then enter license
key. Use the license key below. NOTE
we only have 10 instances of this key
862001140448
Now you should see a larger circuit
frame with a chassis ground symbol in the
middle of the screen.
Create the following circuit in easy circuit:
 Click and drag elements from the
tool bar into the main area.
 Use the Rotate Tool to rotate
circuit elements

Use the adjust tool
to
change the value of circuit
elements.
Note this is the same circuit that you analyzed last Thursday in
the Mesh analysis lab.
 Once you have completed drawing the circuit click the
transient analysis tool
simulation.
to see the circuit
Make sure that your values match those shown at right
and take a screen shot for your blog.
Thevenin’s Theorem
It often occurs in practice that a particular element in a circuit is variable (usually called
the load) while other elements are fixed. As a typical example, a household outlet
terminal may be connected to different
appliances constituting a variable load. Each
time the variable element is changed, the entire
circuit has to be analyzed all over again. To
avoid this problem, Thevenin’s theorem
provides a technique by which the fixed part of
the circuit is replaced by an equivalent circuit.
According to Thevenin’s theorem, the linear
circuit in Fig. (a) can be replaced by that in (b).
(The load in the figure may be a single resistor
or another circuit.)
The circuit to the left of the terminals a-b in (b)
is known as the Thevenin equivalent circuit; it
was developed in 1883 by M. Leon Thevenin
(1857–1926), a French telegraph engineer.
Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an
equivalent circuit consisting of a voltage source VTh in series with
a resistor RTh , where VTh is the open-circuit voltage at the terminals and RTh is the input
or equivalent resistance at the terminals when the independent sources are turned off.
Our major concern right now is how to find the Thevenin equivalent voltage VTh and
resistance RTh . To do so, suppose the two circuits above are equivalent. Two circuits
are said to be equivalent if they have the same voltage-current relation at their terminals.
Let us find out what will make the two circuits equivalent. If the terminals a-b are made
open-circuited (by removing the load), no current flows, so that the open-circuit voltage
across the terminals a-b in (a) must be equal to the voltage source VTh in (b), since the
two circuits are equivalent. Thus VTh is the open-circuit voltage across the terminals as
shown in (a) below; that is,
VTh = voc
Again, with the load disconnected and terminals a-b open-circuited, we turn off all
independent sources. The input resistance (or equivalent resistance) of the dead circuit at
the terminals a-b in (a) must be equal to RTh in (b) because the two circuits are
equivalent.
Thus, RTh is the input resistance at the terminals when the independent sources are turned
off, as shown in (b); that is,
RTh = R in
To apply this idea in finding the Thevenin resistance RTh , we need to consider two cases.
CASE 1 If the network has no dependent sources, we turn
off all independent sources. RTh is the input resistance of the
network looking between terminals a and b.
CASE 2 If the network has dependent sources, we turn off
all independent sources. As with superposition, dependent
sources are not to be turned off because they are controlled by
circuit variables. We apply a voltage source v o at terminals a
and b and determine the resulting current io . Then RTh = vo /io,
as shown in (a) below. Alternatively, we may insert a current
source i o at terminals a-b as shown in (b) and find the terminal
voltage vo . Again RTh = vo /io . Either of the two approaches
will give the same result. In either approach we may assume
any value of vo and io . For example, we may use vo = 1 V or io
= 1 A, or even use unspecified values of vo or io .
It often occurs that RTh takes a negative value. In this case, the
negative resistance (v = − iR) implies that the circuit is
supplying power.
Thevenin’s theorem is very important in circuit analysis. It
helps simplify a circuit. A large circuit may be replaced by a
single independent voltage source and a single resistor. This
replacement technique is a powerful tool in circuit design.
As mentioned earlier, a linear circuit with a variable load can
be replaced by the Thevenin equivalent, exclusive of the load.
The equivalent network behaves the same way externally as
the original circuit. Consider a linear circuit terminated by a
load RL , as shown.
The current IL through the load and the voltage VL across the
load are easily determined once the Thevenin equivalent of the
circuit at the load’s terminals is obtained, as shown in (b).
From (b), we obtain
Example:
We will use practice using Everycircuit and find the current
through the resistor RL below given the that the value of RL =
6.
Quickly draw the circuit in Everycircuit and determine the value of the current through
RL.
Find the Thevenin equivalent circuit of the circuit shown to the left of the terminals a-b.
Then find the current through RL = 6, 16, and 36 ohm.
We find RTh by turning off the 32-V voltage source (replacing it with a short circuit) and
the 2-A current source (replacing it with an open circuit). The circuit becomes what is
shown
Rth = 4 || 12 + 1 = 3 + 1 = 4 Ohms
To find Vth we open circuit the load as shown below:
Now we apply mesh analysis to find the voltage across the 12Ohm resistor which must be
the Vth.
− 32 + 4i 1 + 12(i 1 − i 2 ) = 0,
i2=−2A
Solving for i 1 , we get i 1 = 0.5 A. Thus,
V Th = 12(i 1 − i 2 ) = 12(0.5 + 2.0) = 30 V
The Thevenin equivalent circuit is shown at right. The current through
RL is
Find the Thevenin Equivalent as seen by R below
+
1. Open circuit the resistor to find Voc = Vth
2. Short circuit the element to Rth
Thevenin's Theorem
Overview:
In this lab, we experimentally investigate Thevenin’s Theorem. We will analytically
determine a Thevenin equivalent for a given circuit; we will then experimentally
determine the Thevenin resistance and the open-circuit voltage necessary to create the
Thevenin equivalent circuit.
We will use the Thevenin equivalent to the given circuit to analytically predict the
voltage which will result from loading the circuit with a resistor. We will then test our
Thevenin equivalent circuit by:
1. connecting the load resistor to the original circuit and measuring the resulting
load voltage, and
2. physically creating the Thevenin equivalent circuit, connecting the load
resistor to this circuit, and measuring the resulting load voltage and
comparing the results obtained with the Thevenin circuit and the original
circuit.
Finally, we will vary the value of the load resistance and measure the power
dissipated by the load resistor as a function of the load resistance. We will use this
result to check our expectations based on the maximum power transfer theorem.
General Discussion:
This lab assignment concerns the circuit
shown in Figure 1 below. We want to
determine the equivalent Thevenin circuit
seen at the terminals a-b.
Pre-lab:
Determine the Thevenin equivalent circuit
(the open circuit voltage VOC and the
Thevenin resistance RTH) seen by a resistor
connected to the terminals a-b of the circuit
of Figure 1. (e.g. determine the Thevenin
equivalent circuit seen by the load resistor
RL.) Sketch the Thevenin equivalent circuit.
Show all work on your whiteboard and
include a picture for your blog.
Setup the circuit in EveryCircuit and using a value of 1K, determine the current through
RL.
Lab Procedures:
1. Choose the six resistors (all resistors except for the resistor RL) in the circuit of
Figure 1. Record the actual resistance values.
2. Assemble the circuit of Figure 1, except for the resistor RL. Measure the open-
circuit voltage (VOC) across the terminals a-b. Also measure the Thevenin
resistance (RTH) seen at the terminals a-b. (You will need to replace the voltage
sources in the circuit with short circuits in order to determine the Thevenin
resistance of the circuit.) Compare these measured values with your
expectations based on the pre-lab analyses, by calculating a percent error
between the actual and theoretical values.
3. Pick a random resistor for the load resistance RL, in the range 4k<RL<10k, and
connect it between the terminals a and b in the circuit of Figure 1. Measure the
voltage across the load resistance and compare this voltage to your expectation
based on the Thevenin equivalent circuit from your pre-lab.
4. Build the Thevenin equivalent circuit you determined in the pre-lab. Load the
Thevenin circuit with the resistor RL you used in part 4 above. Measure the
voltage across the load resistor and compare it to the voltage you measured in
part 4. (e.g. compute a percent difference between the load voltage produced
by the original circuit and the Thevenin equivalent circuit.)
5. Connect a potentiometer between the terminals a-b. Measure and record the
load voltage as a function of potentiometer resistance. Calculate the power
delivered to the Vload a function of the load resistance. Plot the load power as
a function of the load resistance and estimate the load resistance which results
in maximum power dissipation by the load. Compare this value from your
expectations based on your Thevenin resistance from the pre-lab and the
maximum power theorem.
Include in your Blog:
1. A sketch of the Thevenin equivalent circuit you determined in the pre-lab. Label the
Thevenin resistance and the open-circuit voltage on your sketch.
2. A schematic of the circuit you implemented in the lab procedures. Label the
schematic with the actual resistance values used.
3. Provide your measured values for the Thevenin resistance and the open-circuit
voltage from part 2 of the lab procedures. Also provide the percent error between
your measured values and your expectations from the pre-lab analysis.
4. In the space below, provide your results from part 3 from the lab assignment,
including:
a. The value of the load resistor you used
b. The measured load resistor voltage
c. Your expected value of the load resistor voltage, based on the Thevenin circuit of
your pre-lab
5. Provide below the measured load voltage from the Thevenin equivalent circuit you
constructed in part 4 of the lab procedures. Also provide the percent difference
between this load voltage and the load voltage from the original circuit (from part 4b
above).
6. Your plot of power vs. load resistance generated in part 5 of the lab procedures.
Provide your estimate (from the data) of the load resistance which draws maximum
power from the circuit.