ECED 2000 Electric Circuits
Laboratory 2000 – 1 Kirchhoff’s Law
Prior to arriving at the laboratory to carry out this experiment analyze the circuit shown
in 1.0 (i) using nodal analysis and enter the values of all voltages and currents which you
have calculated in the table below under the heading “Calculated”. Remember to record
polarities (+ or -) (You can use a circuit solver if you have access to one).
Quantity
V1
V2
V3
V4
V5
Calculated
Measured
% Difference
I1
I2
I3
I4
I5
To verify that your calculations are correct check that each of the following equations
approximates zero.
KCL: (i) I1 + I2 + I3 = 0, (ii) I3 + I4 + I5 = 0
KVL: (iii) 12 – V1 – V2 = 0, (iv) V2 – V3 – V4 = 0, (v) V4 – V5 – 6 = 0
DALHOUSIE UNIVERSITY
Department of Electrical and Computer Engineering
ECED 2000 Electric Circuits
Laboratory 2000-1 Kirchhoff's Laws
Object:
-To seek an experimental verification of Kirchhoff's Laws
-To note the difference between measurement and modeling errors
Equipment:
Device components labeled 1- 5
Breadboard (1)
Digital Multimeter (1)
Dual Power Supply (1)
Introduction:
1.0
Fundamental Laws: There are two sets of laws upon which all electric circuit analysis is
based. These laws are:
1) Element Laws - these provide the relationship between the voltage across the particular
element and the current through the element. These laws are most frequently described by
a mathematical equation (e.g. Ohm's Law v = i r) or a graphical relationship (eg. Diode
characteristic);
2) Laws of Interconnection or Kirchhoff's Laws - These laws relate the currents and
voltages of all/circuit elements and are based on the way in which the elements are
connected.
Kirchhoff's Laws: The two laws, which were formulated by Kirchhoff, are as follows:
Kirchhoff's Current Law (KCL): For any lumped parameter network, for any node, for all
time, the algebraic sum of all the currents entering (or leaving) the node is zero. This is a
statement of conservation of charge where no node can store or radiate a charge.
Kirchhoff's Voltage Law (KVL): For any lumped parameter network, for any loop, for all time,
the algebraic sum of the voltages around the loop is zero. This is a statement of conservation of
energy.
Experiment:
1.0
Verification of Kirchhoff's Laws
i)
Connect the network as shown below.
I1
I3
100 Ω
1
I2
+ V1 -
330 Ω
3
I5
+ V3 -
I4
2
V2
-
470 Ω
4
V4
6V
-
-
2.0
+ V5
+
+
750 Ω
12 V
330 Ω
5
ii)
Ensure that the two sources are supplying the correct voltage by measuring the
terminal voltage after they are connected to the network. Why does it have to be
checked after connection is made?
iii)
With the multimeter set to DC Volts measure and record all specified voltages
with polarity as marked.
iv)
With the multimeter set to DC Amps measure and record all specified currents
with the direction as marked.
v)
Using the tabulation sheet provided sum the measured currents and voltages for
each loop and node. Kirchhoff says that all the sums should be zero. If they are
not, why not? Does the insertion of the meter result in any error? What would you
look for in a) a good voltmeter and b) a good ammeter?
vi)
Check the power dissipation in the elements against the power supplied by the
source. Are they the same? If not, why not?
Circuit Analysis
i)
Apply both mesh and nodal analysis to determine the circuit voltages and
currents. Do the analytical results match the measured results? If not, why not?
ii)
Try to simulate the circuit above using a circuit solver (here’s one :
https://www.circuitlab.com/) and record in a table all currents and voltages
obtained from the analysis of the simulated circuit.
iii)
3.0
Non-Linear Elements
i)
4.0
From your measured values of voltage and current, determine the resistance of
each element. What is the tolerance level of the resistance coding?
A diode is a semiconductor device that conducts current in one direction only.
Remove element 3 from your circuit and replace it with element 6 (the diode).
Make sure the end of the diode with the dark band points toward the 6 V source.
Repeat the steps of part 1. Do Kirchhoffs Laws still hold?
Report
i)
Report your work in the format described in class. Your conclusions should
contain a discussion of sources of error, including measurement error and
modeling error, as well as answers to the questions posed in the procedure.
R 1 = _________
I1
R 3 = _________
I3
b
R 5 = _________
5
3
1
b'
Node b
I2
I1
I4
Node c
I3
h
j
c'
CutSet b' h j c'
I1
I4
I2
I3
I5
- I4
Sum
Sum
I2
- I5
Sum
a
2
VS1 = _________
e
I5
c
R 2 = _________
4
Mesh b c e b
Mesh a b e a
V ab
e
Mesh c d e c
V cd
V be
V ce
V de
V ea
V eb
V ec
Sum
Sum
Sum
e
Loop a b c d e a
VS2 = _________
R 4 = _________
V bc
Loop a b c e a
d
e
Loop b c d e b
PR1
PR2
PR3
PR4
PR5
Sum
Sum
Sum
Kirchhoff’s Laws Tabulation Sheet
Sum
PVS1 +PVs2