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Ohm's Law
Purpose
a. To verify Ohm’s law.
b. To compare the potential vs. current behavior of a resistor to that of a light bulb.
c. To determine the equivalent resistance of combinations of resistors by current-voltage
method.
Theory
The fundamental relationship among the three important electrical quantities current , voltage , and resistance was discovered by Georg Simon Ohm. The relationship and the unit of electrical resistance were both named for him to commemorate this contribution to physics. One statement of Ohm’s law is that the current (I) through a resistor is proportional to the potential difference (V) across the resistor. Ohms law is normally written as
V IR (1)
where R is the resistance of the resistor in Ohm () when potential difference (V) is in Volt and current (I) in Ampere (A). Resistance is a measure of how difficulty to flow current through the device.
In this experiment you will verify Ohm’s law in several different circuits using a Current Probe and a Voltage Probe. Any device that obeys Ohm’s law showing linear relationship of V and I is called Ohmic device, otherwise non-ohmic device.
You will also apply Ohm’s law to determine the equivalent resistance of resistors connected in different combinations. Fig. 1a shows the resistors connected in series and Fig. 1b shows the resistors connected in parallel.
Equivalent resistance ( Req ) in series combination of resistors is given by
and equivalent resistance ( Req ) in parallel
combination of resistors is given by
Apparatus
Vernier Circuit board, LabQuest interface device, current probe, voltage probe, computer with Logger Pro, Power supply, light bulb (6.3 V), digital multimeter.
Fig. 1a. Series combination of resistors
Fig. 1b. Parallel combination of resistors
Req R 1 R 2 R 3 ...
1 2 3
Req R R R
a b
a
b
Description of Apparatus
We are going to use a Vernier Circuit Board-2 as shown in Fig. 2 for this experiment. The circuit board contains resistors, capacitors, an LED, switches, battery clips, connections for external power, a resettable fuse, connections for the addition of other components, and turreted test points for easy connection of alligator-clip test leads. The Vernier circuit board is designed for use in the study of simple electric circuits.
We will be using resisters and light bulb holders in the circuit board for this laboratory. A DC power supply with variable output, Vernier voltage probe and current probes will be used for measurements. These probes must be connected to a Vernier Lab Quest which may be connected to a computer. Vernier Logger Pro software will be used for collecting and analyzing the data.
Basic circuit diagram for this lab is shown in Fig. 3a. A resistor (a and b are terminals of the resistor) is connected to a variable power supply to change the current through the resistor. In order to measure the current an ammeter is connected in series and to measure potential difference a voltmeter is connected in parallel.
Why are the ammeter connected in series and voltmeter in parallel to the resistor? As we are using a variable power supply, voltage and current sensors and Vernier apparatus, our real circuit connection will look line in Fig 3b. CS is the current sensor and VS is the voltage sensor. The arrow in the CS indicates the direction of current when the reading is positive. Voltage sensor reads positive when the potential at the red terminal is higher than that at the black terminal.
Fig. 2. Vernier Circuit board
Fig. 3a. Basic Circuit diagram
+
-
Red
Black
CS
Power supply
Red Black
VS
LabQuest
Fig. 3b. Sketch of circuit connection
a
b
- To view a single graph of potential vs. current, choose Show Graph ► Graph 1 from the Graph menu. a. Change the y-axis (the vertical axis) to Voltage. b. Change the x-axis to Current. The new plot appeared is the V-I curve. [Short cut: click at Event on horizontal axis of Potential graph and select Current ] Are the voltage and current proportional for this resistor? If so, fit a straight line to the data using Linear Curve Fit under the Analyze menu. Record the slope and y -intercept of the regression line in table 1, along with their units. You should include the graph in your report. What is the physical significance of these values?
- Now, repeat the previous Steps 1 – 7 using a different resistor in the circuit board. Analyze the V-I curve and record the data in table 1. What will happen to the V-I curves if the current in the circuit is reversed?
Part II. Potential difference (V) versus current (I) behavior in a light bulb
In this part of the experiment, you ae going to investigate the potential vs. current behavior of a light bulb and compare it to a resistor you just found.
- Insert a 6.3 light bulb in one of the light bulb holder on the circuit board. Replace the resistor in the circuit with the light bulb. Repeat Steps 2–7, but this time, increase the voltage in 0.1 V steps up to 1.0 V, 0.5 V steps from 1 to 4 V, and in 0.1 V steps again from 4 to 5 V.
- To examine the graph, tap any data point. As you tap each data point, the values of current and voltage will be displayed on the graph. Is the slope constant? To compare slopes of data at different parts of the curve, estimate the slope at the start of the graph (the low-current end) using the second and third points. Record the slope in the data table. Be sure to enter the units of the slope. In the same way estimate the slope using the last two points. Record this slope in the data table. You should include the graph in your report. What do you expect if the current in the circuit is reversed?
Part III. Equivalent resistance in series and parallel combinations
You should have observed that resistors obey Ohm’s law thus the resistors are Ohmic device. Resistance, R , is defined using R = V / I. The resistance could be due to a single resistor or several resistors connected in different configuration. In this part of the experiment, you are going to determine the equivalent resistance of the resistors connected in a series, a parallel and a mixed combinations.
a. Series combination
- In the circuit board, connect three resistors (two 10 and one 51 ) in series as in the circuit shown in Fig. 1a using connecting wires. Make sure you identify the terminals a and b of this combination. (Note: terminals of this combination is same as the terminals of a single resistor or a bulb).
- Measure the resistance of the combination using the digital multimeter and record in table 2.
- Now connect the terminals of this combination in your previous circuit to measure potential and current. Have your instructor check the circuit before proceeding.
- Repeat Steps 2–7 of Part I. Record the value of slope in table 2.
b. Parallel combination
- Now, remove all the wires used to prepare the previous combination of resistors and prepare a parallel combination of three resistors (two 10 and one 51 using connecting wires. Make sure to identify the terminals of the combination. You may connect two wires at the terminal for terminals a and b.
- Measure the resistance of the combination using the digital multimeter and record in table 2.
- Now connect the terminals of this combination in your previous circuit to measure potential and current. Have your instructor check the circuit before proceeding.
- Repeat Steps 2–7 of Part I. Take the data only up to 3 V. Record the value of slope in table 2.
c. Mixed combination
- Now construct a new circuit on the circuit board with a combination of resistors as shown in the Fig. 4. Measure the resistance of the combination across the terminals a and b using the digital multimeter.
- Connect the terminals a and b to your previous circuit to measure potential and current.
- Repeat Steps 2–7 of Part I. Take the data only up to 3 V. Record the value of slope in table 2.
COMPUTATION AND ANALYSIS
Part I
- From your observation, is there a proportional relationship between voltage and current?
Compare your observation with the resistors and the light bulb.
- In case of the resistors, how close is the y-intercept to zero? What is the significance of having the y-intercept close to zero?
- Compare the value of the slope you determined in each fitting to the resistance of each resistor. Resistors are manufactured such that their actual value is within a tolerance. For most resistors the tolerance is 5% or 10%. Check with your instructor to determine the tolerance of the
10 (^51)
51
68
a b Fig. 4. Combination of resistors
Data Sheet Date experiment performed:
Name of the group members:
Table 1. Potential vs. current
Part I and II
Slope of regression line (V/A)
Y-intercept of regression line (V)
Resistor
Resistor
Light bulb (low current)
Light bulb (high current)
Table 1. Equivalent resistance
Part III
Resistors
used
Combination Resistance from
multimeter
Resistance from
the slope of the
V-I curve
Calculated
resistance
Series
Parallel
Mixed
