Experiment
2
OHM’S LAW AND RESISTANCE
Objective
To illustrate the voltmeter-ammeter method of measuring electrical resistance and to verify
Ohm's Law.
Physical Principles
Materials containing mobile electric charges (usually electrons) are called conductors.
In
contrast, the materials, all electric charges in which are fixed and cannot be moved freely are
called insulators. Applying electric field on a conductor results in mechanical motion of the
mobile charges in a particular direction. This directional motion of electric charges is called
electric current. The applied electric field is characterized by the difference of electric potential V
along the conductor. Potential difference, or voltage, is measured in volts, V. Electric current I
is defined as the amount of charge transferred through conductor in one second. Electric current
is measured in amperes, A. For most conductors, electric current is proportional to the applied
voltage. This linear relation between V and I is known as Ohms’ Law:
where S is the conductance of the conductor. Conductance describes the ability of conductor to
conduct current. In practice, more common parameter describing electrical properties of
conductors is resistance R, which is inverse value of conductance:
The unit of resistance is ohm, Ω. Now the Ohm's law can be re-written in terms of resistance:
or
Conductors, resistance of which does not depend on either V or I are called ohmic conductors.
Otherwise they are non-ohmic conductors. Most metals are ohmic conductors, whereas
semiconductors and many conductive ceramics are non-ohmic conductors. Resistance of a
conductor depends on various factors, e.g. the material the conductor is made of, its shape and
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Ohm’s Law and Resistance
size, the direction of electric current flow, temperature. For ohmic conductors, graphing V vs I, in
Cartesian coordinates yields a straight line whose slope is R (Fig. 1).
y=mx
m=100.5+/-0.253
slope R 
V
I
V
I
Fig. 1. Voltage applied to a conductor as a function of the induced current for an ohmic
conductor. Slope of this dependence calculated as the change of voltage V divided by the
corresponding change of current I equals resistance R of this conductor: R=V/I.
The ability of moving electrons to maneuver through a conducting material depends on physical
parameters of this material and on its temperature. Heating results in thermal agitation of moving
electrons and the atoms constituting the conductor. This agitation retards the directional motion
of electrons and, consequently, increases resistance of the conductor.
Variations in room
temperature, which are usually small, are not alone responsible for the changes in the conductor's
temperature. The current flow itself can increase temperature considerably: the greater the
current in a conductor the higher its temperature. The actual dependence of resistance on
temperature is a characteristic of the conducting material. It is measured by so-called temperature
coefficient of resistivity α. This coefficient may be positive or negative and therefore the
resistance of some conductors increases with temperature, whereas it decreases for the others.
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Ohm’s Law and Resistance
For instance, for tungsten α = +4.5×10-3 °C-1, for carbon (graphite) α = -5×10-4 °C-1. The change
of resistance with temperature is given by the following formula:
[
]
where R(T) is the resistance at temperature T, RRT is the resistance at room temperature, TRT is
room temperature (usually 20°C).
Apparatus
- Variable DC power supply
- Ammeter (Digital Multimeter set to mA DC)
- Voltmeter (Digital Multimeter set to V DC)
- 100 ohm tubular resistor
- 100 watt tungsten filament lamp
- 32 cp carbon filament lamp
- Lamp socket
- Connecting wires
- Throw switch
- Spades
Procedure
1. Set up the equipment as shown in Fig 2 with 100Ω tubular resistor for R, a digital multimeter
(connect to the 400mA input and set the dial to mA, press the yellow button to switch from
AC to DC) for A, and a second digital multimeter for V (set the dial to V DC). Have your
connections checked by your technician/instructor before turning on the power supply.
Close the circuit and vary voltage in 2V steps, recording V and I for each step. Perform the
measurements at least three times.
2. Open the circuit and replace the tubular resistor with the 100 watt tungsten filament lamp for
R. Have your connections checked by your technician/instructor before turning on the
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Ohm’s Law and Resistance
power supply. Close the circuit and vary voltage in 2 V steps, recording V and I for each step.
Perform the measurements at least three times.
3. Open the circuit and remove the 100W bulb and place the 32cp carbon filament lamp for R.
Have your connections checked by your technician/instructor before turning on the power
supply. Close the circuit and vary voltage in 2 V steps, recording V and I for each step.
Perform the measurements at least three times.
Voltmeter
V DC
Ammeter
+ V
V
+ A
A DC
Power supply
-
V
400mA
A
mA
R
Resistor
Switch
Fig. 2. Circuit set-up used for the study of Ohm's Law by voltmeter-ammeter method.
Multimeter
set to mA DC
Multimeter
set to V DC
400mA
Input
Power Supply
R
100W Tungsten
Lamp
Switch
Circuit is closed and current is allowed to flow through the
circuit. Current I through the circuit as well as voltage V
across the resistor can be recorded.
Open the circuit before changing resistors.
Fig. 3 – Circuit with 100W Bulb in place for R
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Ohm’s Law and Resistance
Calculations and Graphs
1. Calculate average values of current for each voltage and corresponding experimental errors.
2. Plot the calculated data for each resistor on a graph using V as the y-axis and I as the x-axis
for each resistor (3 curves in one graph). See Fig. 4 for sample graph.
3. On the graph, fit the points for 100 ohm resistor with a straight line. Find the slope of this
line. Compare the found value with the rated resistance 100 ohm.
4. Calculate resistance of 100 ohm resistor using your data for each voltage step. Find average
value of the resistance and its experimental error. Compare the calculated value with that
obtained from the graph.
3. From the data of the Procedures 2 and 3 compute R for each pair of V and I for tungsten and
carbon lamps. Plot R as a function of I for both lamps. See Fig. 5 for sample graph.
Sample Data
Autofit for: 100 Resistor | V
V = mI
m: 101.6 +/- 0.053
Fig. 4. Sample data of V vs I for ohmic and non-ohmic resitors
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Ohm’s Law and Resistance
Fig. 5. Sample data of R vs I for ohmic and non-ohmic resistors
Questions
1. Of the three objects you measured in this experiment (tubular resistor and two lamps), which
are ohmic resistors and which are not?
2. What is your explanation for the fact that the current induced in the lamps does not follow
Ohm’s Law?
3. What do the plots tell you about the temperature coefficient of resistivity of each object
used?
4. Using formula (4) evaluate the maximum temperature the filaments in the lamps reach during
the measurements.
5. Predict current, which would be induced in the resistors you measured when a voltage of 40
V could be applied.
Illustrations provided by Jackeline S. Figueroa
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