İzmir University of Economics
EEE201 Electrical Circuits I Lab
EXPERIMENT IV:
Kirchhoff's Voltage Law
Objective:
The students will be able to learn:

How to measure node voltages, voltages related to (simple) closed node sequences and,
in particular, to closed paths (also called as loops or meshes), in a given circuit for
verifying that Kirchoff's Law Law is satisfied.

How to find all voltages in a circuit with a minimum number of voltage measurements,
i.e. by measuring independent voltages.
A. Pre-lab Tasks
•
•
•
Read Chapter 3 of the book by Dorf & Svoboda and also Chapter 1 of the book by L. O.
Chua, C. Desoer and E. Kuh.
Read the background material provided below.
Complete the pre-lab assignment. (You should submit it at the beginning of the lab
session.)
Pre-lab assignment:
Consider the circuit given in Figure 1.
1
+ V1 -
R1
VS
+ V3 -
2
R2
4
+
V2
-
R3
R4
3
+
V4
-
Figure 1. A four-node and two-loop circuit consisting of five circuit elements





Write down Kirchoff's Voltage Law equations for all simple closed node sequences
and loops.
Choosing the fourth node as the reference, write the element voltages in terms of the
node voltages in the matrix form.
 Compare the matrix representing element voltages as node voltage
differences to the so-called incidence matrix which represents the KCL
equations for the nodes excluding the reference one.
 Specify a suitable closed node sequence for each element voltage in
order to give its representation in terms of the node voltages. Then,
explain whether or not the KVL equations providing the element
voltages in terms of the node voltages are sufficient to write all KVL
equations.
Assigning a directed edge for each two-terminal element, obtain a directed graph for
the circuit in Figure 1. Use edge directions as compatible to the element voltage
polarities.

Specify all trees for the obtained directed graph.
Labeling branches and links in a chosen tree, determine a set of independent
element voltages and also the complementary set of element dependent voltages.
Propose a way of measuring all of the element voltages in the given circuit by
voltmeter with a minimum number of voltage measurements.
1-1
References:



R. C. Dorf & J. A. Svoboda, Introduction to Electric Circuits, 8th Edition, Wiley, 2011.
L. O. Chua, C. Desoer and E. Kuh, Linear and Nonliear Circuits, McGraw Hill, 1987
P. M. Jansson, Networks-I, Lecture Slides on http://users.rowan.edu/~jansson/ (15:00,
27.09.2011)
B. Background
As introduced in Experiment 3, the German physicist Gustav Robert Kirchhoff stated two rules
regarding the behavior of electrical circuits. The first rule, known as Kirchhoff’s Current Law
(KCL), is about the currents entering and exiting a node. The second rule is known as
Kirchhoff’s Voltage Law (KVL). KVL states that “the sum of the element voltages around any
closed path in a circuit is equal to zero”.
The above statement of KVL originally postulated for a circuit consisting of 2-terminal elements
and is valid more generally for planar circuits whose graphs can be drawn in the plane without
having a cross cutting. Then, KVL statement is generalized along the development of circuit
theory into the non-planar circuits: “Algebraic sum of all (node) voltage differences associated
to a (simple) closed node sequence must be equal to zero for all time t such that the voltages
whose polarities are compatible to the direction of the node sequence have positive signs in the
sum while the voltages with non-compatible directions have negative signs. Where, the simple
closed sequence is a node sequence whose first and last nodes are the same and all other nodes
appear once in the sequence.” KVL is, indeed, is a direct consequence of the conservation of
fluxes along a closed path.
The KVL expression around the closed loop for the following circuit is: v1 + v2 + v0 – vs = 0
+ v1 -
+ v2 -
vS
+
v0
-
IS
Figure 2. A circuit made of 2-terminal elements
Note that the voltage of the independent current source appears in the KVL equation not its
current whose value is known.
I9
6
5
4
I6
I8
I1
V1
I2
1
I5
I7
I4
2
3
I3
Figure 3. A non-planar circuit
It can be seen from Figure 3 that KVL equation v1-4 + v4-3 + v3-1 = 0 associated to the simple
closed node sequence 1-4-3-1 cannot be obtained from KVL equations written for meshes.
1-2
C. In-Lab Experimental Work
Task C.1.1.: Build the below circuit on the protoboard available in Yıldırım Electronics Basic
Training Set Y-0016. Choose the resistance values as R1 = R2 = R3 = R4 = R5 = R6 = R7 = 330 Ω.
Adjust the power supply as Vs = 10 Volts.
1
I1
3 I6
2 I4
I2
R2
V1
R4
I3
R3
I5
4
R6
R5
I7
R7
5
Task C.1.2.: Choose a set of independent element voltages. Measure the independent element
voltages by a voltmeter and then calculate the remaining (dependent) element voltages by KVL
node equations.
Table 1
Independent
Voltages
(Measured)
Dependent
Voltages
(Calculated)
Task C.1.3.: Now, measure the dependent voltages by using voltmeter and check whether or
not they are identical to the ones found by calculation in Task C.1.2.
Table 2
Dependent
Voltages
(Measured)
Dependent
Voltages
(Calculated)
Task C.1.4.: Calculate the V3/V1, V5/V3, V5/V1, V7/V5 V7/V1 ratios from the values measured in
Tasks C.1.2 and C.1.3. What do you think about the dependency of these ratios on the
resistance values of the resistors and the values of independent voltage source V 1? Justify your
answer by conducting appropriate experiments.
Table 3
V3/V1
V5/V3
V5/V1
V7/V5
V7/V1
1-3
Task C.1.5.: Repeat the measurements and calculations in Tasks C.1.2 and C.1.3 for another
pair of independent and dependent voltage sets.
Table 4
Independent
Voltages
(Measured)
Dependent
Voltages
(Calculated)
Table 5
Dependent
Voltages
(Measured)
Dependent
Voltages
(Calculated)
Task C.1.6.: Assume that V2, V4 and V6 element voltages can be measured in a direct way
whereas all other element voltages cannot be. (Such situations may arise in circuits where a
part of the circuit elements could not be reachable due to long distances among circuit elements
or due to some other physical limits.) Measure V1, V2, V4 and V6 element voltages and then
calculate V3, V5 and V7 by choosing an appropriate KVL equation. Do not use more than one KVL
equation.
Table 6
Measured
Voltages
V1=
V2=
V4=
Calculated
Voltages
V3=
V5=
V7=
V6=
D. Post-Lab Tasks: Lab Report
The lab report should have the information contained in the pre-lab assignment and also the
answers of the following questions. The lab report should be submitted at the beginning of the
succeeding lab session.


Explain
o What you have done in this lab.
o How do you measure the quantities related to the the experiment.
Reply the questions in the Tasks C.1.2-C.1.6.
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