LAB 5: KIRCHHOFF’S LAWS
Simple electrical networks, involving only
resistors and a single voltage source, can
usually be solved (often by inspection alone) by
network reduction schemes: replacing parallel
and series combinations with their equivalent
resistance. Some configurations, though, are
neither parallel or series arrangements and
require more powerful (complicated) methods of
analysis. These methods are usually covered in
higher level courses. Kirchhoff’s Laws give a
simple approach to solving these type of circuits,
though the algebra is often somewhat tedious.
THEORY____________________________________________________
that the sum of all the voltage ‘drops’ around a
‘closed’ path sum up to equal zero. This is an
obvious consequence of the fact that the
potential difference between two points is
independent of the path taken. The purpose of
this lab is to verify Kirchhoff’s laws by making
measurements on the circuit shown below.
The readings of the three ammeters will be
recorded to the nearest 0.05 A. The COMMON
terminal of a voltmeter (typically the black lead)
is connected to point “x” , defining the potential
at that point to be zero. The voltmeter is to be
used to measure the potential at the other
marked points, “a”, “b”, and “c”.
Kirchhoff’s Current Law (KCL) simply states that
the current(s) entering a junction (node) equals
the current(s) leaving the junction. Remember
that a junction is anywhere that the current can
‘split’. Along a branch, between two junctions,
the current must be constant anywhere along
the branch, thus it does not matter where in the
branch the ammeter is inserted. Since electric
current consists of electrons (which are real,
physical) flowing along the conductor, it should
be obvious that they neither multiply nor
diminish ; hence KCL should be obvious to the
student. Kirchhoff’s Voltage Law (KVL) states
+
I1
a
R1
A1
V1
x
+
R2
I2
A2
b
V2
c
R3
+
A3
I3
PROCEDURE________________________________________________
1. Set V1 = 7 v, V2 = 5 v, R1 = 20  , R2 = 5  , and R3 = 15  . Measure Va, Vb, and Vc. Measure I1,
I2, and I3. Record all of these measurements.
2. Change voltages to V1 = 5 v, V2 = 7 v. Leave the resistances as before. Measure and record all
voltages and currents.
1
DATA_______________________________________________________
Va
Vb
Vc
I1
I2
I3
Procedure 1
Procedure 2
KIRCHHOFF’S VOLTAGE LAW
3. Using the data gathered, start with the Top Loop: Start at point “a”, go clockwise, and calculate the
change in potential across each element.
Procedure #1 Vb - Va = ______v ;
Vx - Vb = _____v ;
Va - Vx = _____v
#2 Vb - Va = ______v ;
Vx - Vb = _____v ;
Va - Vx = _____v
What can you conclude about the algebraic sum of the changes in potential around the top loop for each
procedure?
Bottom Loop: Start at point “x”, go clockwise, and calculate the change in potential across each element.
#1
Vb - Vx = ______v ;
Vc - Vb = ______v ;
Vx - Vc = ______v
#2
Vb - Vx= ______v ;
Vc - Vb = ______v ;
Vx - Vc = ______v
What can you concluded about the algebraic sum of the changes in potential around the bottom loop for
each procedure?
Outer Loop: Start at point “a”, go clockwise, and calculate the change in potential across each element.
#1
Vb - Va = _____v ;
Vc - Vb = ______v
Vx - Vc = _____v ;
Va - Vx = ______v
# 2 Vb - Va = ______v ;
Vc - Vb = ______v
Vx - Vc = ______v ;
Va - Vx = ______v
What can you conclude about the algebraic sum of the changes in potential around the outer loop for
each procedure?
2
KIRCHHOFF’S CURRENT LAW
Procedure #1
Procedure #2
Identify currents
entering junctions b
What are the sum of
these currents?
Identify currents
leaving junction b
What is the sum of
these currents?
What conclusion can you make about the sum of the currents entering and leaving a junction?
For Procedure #1, use Kirchhoff’s Voltage and Current Laws to calculate theoretically the currents in each
of the branches of the circuit. Compare these calculated values to your experimental values. Calculate
the percent difference.
Theoretical
Experimental
I1
I2
I3
3
Percent Difference