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Ohm's Law, Kirchoff’s Laws, and Equivalent Resistance©98
Experiment 5
Objective: To build simple electrical circuits and use electrical multimeters to verify
Ohm's law and Kirchoff’s Laws. Make electrical measurements to find the rules for
equivalent resistance.
DISCUSSION:
Electrical circuits behave like an enclosed plumbing system, such as the
circulatory system of the body. There is an "electron pump", which is analogous to the
heart in its function. This pump may be a dry cell, battery, or generator. There is a fluid
of electrons, analogous to the blood. There are wires or conductors, analogous to the
arteries and veins.
A battery, or electrochemical cell, can be used as a source of electrons that will
flow through the wires. Via oxidation and reduction reactions at the two separate
electrode surfaces in a battery, electrons are deposited at one electrode to flow to the
other electrode through a wire.
Ohm's law states that the voltage difference V between two points in a conducting
medium is proportional to the current I between those points. That is,
V  IR
(1)
where the resistance R is a constant of proportionality. Ohm's law states, in other words,
that the resistance between the points is constant. (Actually, Ohm's law is not exactly true
in many cases, and in some cases it fails completely.)
Kirchoff’s laws involve conservation of charge and conservation of energy. The
first law states that if a circuit branches into two different paths the current entering the
junction must equal the current leaving the junction (no charge can be created or
destroyed at the junction). In quantitative terms
Itotal = I1 + I2
(2)
The second law states that the total voltage drop across two or more circuit
elements (resistors, capacitors, etc.) in series must be equal to the sum of the voltage
drops across each circuit element. In quantitative terms
Vtotal = V1 + V2
(3)
If several resistors are connected in series, the effective resistance of the
combination is equal to the sum of the individual resistances of the resistors. That is,
(4)
RTotal  R1  R2  R3  
where RTotal is the effective resistance, and R1, R2, R3, are the individual resistances.
5-1
It can also be shown that if several resistors are connected in parallel, the effective
resistance, RTotal of the combination is given by
1
RTotal

1
1

R1

R2
1

(5)
R3
EXERCISES:
1. Build the following circuits and describe what you read from the meter in terms of
Ohm’s law.
a. The voltmeter is parallel to the wire running from the 100  resistor to the
rheostat. What voltage drop do you expect?
V
+
_
+
Variable
Resistance
b. The voltmeter measures the voltage drop first across one resistor, then across
another resistor in series with the first, and then across the combination. How is
the 3rd measurement related to the first two?
1st Measurement
+
V
2nd Measurement
_
+
V
_
V
_
+
3rd Measurement
+
+
+
c. The ammeter measures the current through one resistor, then through another
resistor in series with the first, and then through the combination. How are the
measurements related to each other?
First measurement
+
Second measurement
+
Third measurement
+
5-2
Use the measurements from parts (b) and (c) to verify Kirchoff’s laws and then use
Ohm’s law to deduce the expression for the equivalent resistance of a series circuit of
resistors, Eq. (4).
d.
Use the ammeter to first measure the current in each resistor separately, then the
current in the parallel resistors. How is the 1st measurement related to other two?
+
A
_
3rd Measurement
2nd Measurement
A
+
_
A
_
1st Measurement
+
+
+
+
e. The voltmeter measures the voltage drop across one resistor, then across another
resistor in parallel with the first, and then through the combination. How are the
measurements related to each other?
V
+
+
V
_
_
+
First measurement
+
Second measurement
+
V
_
Third measurement
+
Use the measurements from parts (d) and (e) and use Ohm’s law to deduce the
expression for the equivalent resistance of a series circuit of resistors, Eq. (5).
2. Build the circuit shown. The rheostat is used to vary the voltage drop across the
resistor R, whose resistance is to be determined graphically. The current in this
resistor (and in the voltmeter) is measured by the ammeter.
+
R
+
_
A
+
V
_
Figure 9: Circuit for Exercise 2.
5-3
a. Using one fixed resistor,
i)
Read the voltage and current readings at one setting of the rheostat.
ii)
Change the rheostat and read the new current and voltage settings.
iii)
Repeat i) and ii) until 5 readings have been taken.
b. Repeat part (a) until you have a set of 5 voltage readings for 5 different resistors.
c. For each resistor, plot the voltage drop across each resistor as a function of the
current in the resistor. After drawing the best straight line through the points for
each resistor, determine the resistance of each by finding the slope of the
appropriate line. (Note: You should have one graph for EACH resistor.)
5-4