İzmir University of Economics
EEE201 Electrical Circuits I Lab
EXPERIMENT 3:
Kirchhoff's Current Law
Objective:
The students will be able to learn:

How to measure currents related to a Gaussian surface and, in particular, to a node, in
a given circuit for verifying that Kirchoff's Current Law is satisfied.

How to find all currents in a circuit with a minimum number of current measurements,
i.e. by measuring independent currents.
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.
Gaussian
Surface - I
1
IS
VS
2 I3
I1
R1
I2
R2
3
R3
I4
R4
4
Figure 1. A four node circuit consisting of five circuit elements
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
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Write down Kirchoff's Current Law equations for all nodes. Then, obtain a matrix
representation for this equation system.
By applying Gauss-Jordan elimination procedure on the matrix obtained above, find a
set of independent currents and also a set of dependent currents.
Propose a way of measuring all of the currents by ammeter with a minimum number
of current measurements.
Obtain the KCL equation for the Gaussian Surface – I in terms of the KCL node
equations.
Explain whether or not the KCL equations for the nodes of the circuit are sufficient to
write all KCL equations from this circuit.
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)
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B. Background
In 1845, a German physicist Gustav Robert Kirchhoff stated two rules regarding
the behavior of electrical circuits: Kirchhoff’s Current Law (KCL) and Kirchhoff’s
Voltage Law (KVL).
The first rule, KCL, is about the currents entering and exiting a node (junction).
KCL states that “sum of all currents entering and the sum of all currents exiting
a node must be equal for all time t”, in other words, “algebraic sum of currents
associated to a node is equal to zero for all time t such that the currents
entering the node have negative signs in the sum while the currents leaving out
of the node have positive signs”.
i4
i5
i3
i6
i2
i1
Figure 2. Currents entering and exiting a node
Consider the above node given in Figure 2.
Currents entering the node: {i1, i2, i4, i6}. & Currents leaving the node: {i3, i5}.
Therefore KCL states that:
i1 (t) + i2 (t) + i4(t) + i6 (t) = i3 (t) + i5(t) for all time t.
This KCL equation can also be written in according to the alternative statement as
i1 (t) + i2 (t) + i4(t) + i6 (t) - i3 (t) - i5(t) = 0 for all time t.
The above statement of KCL originally postulated for a circuit consisting of 2-terminal elements
only is generalized along the development of circuit theory into the circuits containing nterminal elements with n>2 as: “Algebraic sum of all currents associated to a Gaussian surface
must be equal to zero for all time t such that the currents entering the Gaussian surface have
negative signs in the sum while the currents leaving out of the Gaussian surface have positive
signs. Where, the Gaussian surface has a balloon like shape having one inside and one outside,
more precisely it encloses a simply connected region which can be shrunk into a single point.”
KCL is, indeed, is a direct consequence of the conservation of charges inside a Gaussian surface.
G1
Vn
In
1
I1
-
Vp
+
-
Ip
R1
I0
I5
Ig
2
IS
VS
2
3
R2
G2
R5
I2
4
Ic
5
I3
I4
R4
R3
I6
Ib
Ie
R6
6
Figure 3. A circuit containing a four terminal element in addition to 2-terminals
It can be seen from Figure 3 that KCL equations for G1 and G2 Gaussian surfaces (which are,
indeed, supernodes) cannot be obtained from the KCL equations related to the nodes.
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C. In-Lab Experimental Work
Task C.1.1.: Build the below circuit on the proto-board available in Yıldırım Electronics Basic
Training Set Y-0016. Choose the resistance values as R1 = R2 = R3 = R4 = 100 ohm. Adjust the
power supply as Vs = 5 Volts.
1
2 I3
I1
IS
VS
R1
I2
R2
3
R3
I4
R4
4
Task C.1.2.: Choose a set of independent currents. Then, measure the independent currents by
an ammeter and calculate the remaining (dependent) currents by KCL node equations.
Task C.1.3.: Now, measure the dependent currents by using ammeter and check whether or not
they are identical to the ones found by calculation in Task C.1.2.
Task C.1.4.: Calculate the I2 / I3 and I2 / I1 ratios from the values measured in Tasks C.1.2 and
C.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 current sets.
Task C.1.6.: Assume that I2 and I4 currents can be measured in a direct way whereas IS, I1 and
I3 currents 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
limits.) For R1 = R2 = R3 = R4 = 100 ohm but with Vs = 2.5 Volts, measure I2 and I4 currents and
then calculate IS, I1 and I3 currents by choosing appropriate Gaussian surfaces. (Do not use
more than one KCL equation in each current calculation.)
Task C.1.7.: Calculate the I2 / I3 and I2 / I1 ratios from the values measured in Tasks C.1.6 and
compare them to the ones obtained in Task C.1.4. Discuss your observations.
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.
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
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.1.7.
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