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Experiment
2-4
Ohm’s Law
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 through a resistor is proportional to the potential difference
across the resistor. In this experiment you will test the correctness of this law in several different
circuits using two multimeters, one set to measure DCA (ammeter) the other DC V (voltmeter).
These electrical quantities can be difficult to understand, because they cannot be observed
directly. To clarify these terms, some people make the comparison between electrical circuits and
water flowing in pipes. Here is a chart of the three electrical units we will study in this
experiment.
Electrical Quantity
Voltage or Potential
Difference
Current
Resistance
Description
Unit
Water Analogy
A measure of the Energy Volt (V)
difference per unit charge
between two points in a
circuit.
A measure of the flow of Ampere (A)
charge in a circuit.
A measure of how
Ohm ()
difficult it is for current to
flow in a circuit.
+
Water Pressure
Amount of water
flowing
A measure of how
difficult it is for water
to flow through a pipe.
-
Current
probe
Resistor
I
Red
Black
Voltage
probe
Figure 1
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Experiment 2-4
OBJECTIVES
 Determine the mathematical relationship between current, potential difference, and
resistance in a simple circuit.
 Compare the potential vs. current behavior of a resistor to that of a light bulb.
MATERIALS
Vernier Circuit Board
clips to hold wires
light bulb
resistors
2 Multimeters
PRELIMINARY SETUP AND QUESTIONS
1. You will have 3 total Volts available in your circuit, calculate the expected current for the
circuit if you have:
a. 1 - 10  resistor
b. 1 - 51  resistor.
c. 1 - 68  resistor.
2. Draw a diagram of what a circuit should look like with a battery, 1 resistor, an ammeter and a
voltmeter.
PROCEDURE
1. Record the value of the resistor in the data table.
2. With the switch set to External, set your meter to measure the resistance of the resistor and
measure the value of the selected resistor.
3. Make a complete circuit using the batteries, circuit board and resistor, and two meters.
a. Set one meter to the appropriate DCV value level and attach it in parallel to the resistor.
b. Set one meter to appropriate DCA value level and attach it in series with the resistor.
4. Switch the switch to 3V and Record readings from voltmeter and ammeter.
5. Repeat Steps 1–4 using a different resistor.
6. Replace the resistor in the circuit with a light bulb. Repeat Steps 3 and 4.
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Circuit Labs
DATA TABLE
Current
Resistor

Resistor

Resistor

Voltage
Light bulb
ANALYSIS
1. As the resistance increased, the current through the resistor should have decreased, dexcribe
the relationship you observed.
2. Make a graph of Current (I) on the y axis vs 1/R on the x axis. You should see a straight
line? What is the slope of that line?
3. Resistance, R, is defined using R = V/I or I = V/R where V is the potential across a resistor,
and I is the current. R is measured in ohms (), where 1  = 1 V/A. The constant you
determined in 2 should be similar to voltage of the system. However, resistors are
manufactured such that their actual value is within a tolerance. For most resistors the
tolerance is 5% or 10%. Compare your measured value of each resistor to the stated value
and determine your measured tolerance. Calculate the range of possible values for each
resistor. Does the constant in each equation fit within the appropriate range of values for each
resistor?
4. Do your resistors follow Ohm’s law? Base your answer on your experimental data.
5. Describe the current and voltage through the light bulb. How did it compare with data found
for each resistor?
6. Assuming your light bulb follows Ohm’s law. Use your graph and calculate its resistance.
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Experiment 2-4
Series and Parallel Circuits
Components in an electrical circuit are in series when they are connected one after the other, so
that the same current flows through both of them. Components are in parallel when they are in
alternate branches of a circuit. Series and parallel circuits function differently. You may have
noticed the differences in electrical circuits you use. When using some decorative holiday light
circuits, if one lamp is removed, the whole string of lamps goes off. These lamps are in series.
When a light bulb is removed in your house, the other lights stay on. Household wiring is
normally in parallel.
You can monitor these circuits using a Current Probe and a Voltage Probe, and see how they
operate. One goal of this experiment is to study circuits made up of two resistors in series or
parallel. You can then use Ohm’s law to determine the equivalent resistance of the two resistors.
OBJECTIVES

To study current flow in series and parallel circuits.
 To study voltages in series and parallel circuits.
 Use Ohm’s law to calculate equivalent resistance of series and parallel circuits.
Series Resistors
Parallel Resistors
MATERIALS
Vernier Circuit Board
two 10  resistors
two 51 resistors
two 68  resistors
Two Multimeters
PRELIMINARY QUESTIONS
1. Using what you know about electricity, hypothesize about how series resistors would affect
current flow. What would you expect the effective resistance of two identical resistors in
series to be, compared to the resistance of a single resistor?
2. Using what you know about electricity, hypothesize about how parallel resistors would affect
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Circuit Labs
current flow. What would you expect the effective resistance of two identical resistors in
parallel to be, compared to the resistance of one alone?
3. Calculate the effective resistance of connecting one of each type of given resistor in series
and then parallel
PROCEDURE
Part I Series Circuits
-
+
1. Connect the series circuit shown in Figure 2 using the
10  resistors for resistor 1 and resistor 2. Connect the two
meters in the circuit to measure current in the system and
voltage across the entire circuit.
RB
RA
2. Reset the circuit to measure the voltage across each
individual resistor in the circuit.
I
Black
Red
3. Repeat Steps 1-2 with a 51  resistor substituted for
resistor 2.
Figure 2
4. Repeat Steps 1-2 with a 51  resistor used for both resistor 1 and resistor 2.
Part II Parallel circuits
5. Connect the parallel circuit shown in Figure 3 using 51 
resistors for both resistor 1 and resistor 2. . Connect the two
meters in the circuit to measure current in the system and
voltage across the entire circuit.
+
6. Reset the circuit to measure the voltage and Current across
each individual resistor in the circuit.
7. Repeat Steps 14–17 with a 68  resistor substituted for
resistor 2.
8. Repeat Steps 14–17 with a 68  resistor used for both
resistor 1 and resistor 2.
-
R1
I
Red
R2
Black
Figure 3
Part III Currents in Series and Parallel circuits
9. For Part III of the experiment, you will use two meters and one of each type of the resistors
10 , 51 , and 68 
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Experiment 2-4
10. Connect the parallel circuit as shown in Figure 5 using the
51  resistor and the 68  resistor in parallel and the 10 
resistor in series.
+
11. Before you make any measurements, predict the currents and
voltage through the three resistors. Will they be the same or
different? Note that the two resistors are not identical in this
parallel circuit.
12.
-
50
I
I
Connect the meters to measure the current and voltage across
the 10 resistor.
68
Figure 5
13.
Reconnect the meters and circuit to measure the current and
voltage across the 51 resistor
13.
Reconnect the meters and circuit to measure the current and voltage across the 68 resistor.
14. .
Reconnect the meters and circuit to measure the current and voltage across the entire circuit
DATA TABLE
Part I Series Circuits
Part I: Series circuits
R1
()
R2
()
1
10
10
2
10
50
3
50
50
I
(A)
V1
(V)
V2
(V)
Req
()
VTOT
(V)
Req
()
VTOT
(V)
Part II: Parallel circuits
R1
()
R2
()
1
50
50
2
50
68
3
68
68
I
(A)
V1
(V)
V2
(V)
R1
()
V
I1
(A)
1
10
2
51
3
68
Circuit
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ANALYSIS
1. Examine the results of Part I. What is the relationship between the three voltage readings: V1,
V2, and VTOT?
2. Using the measurements you have made above and your knowledge of Ohm’s law, calculate
the equivalent resistance (Req) of the circuit for each of the three series circuits you tested.
3. Study the equivalent resistance readings for the series circuits. Can you come up with a rule
for the equivalent resistance (Req) of a series circuit with two resistors?
4. For each of the three series circuits, compare the experimental results with the resistance
calculated using your rule. In evaluating your results, consider the tolerance of each resistor
by using the minimum and maximum values in your calculations.
5. Using the measurements you have made above and your knowledge of Ohm’s law, calculate
the equivalent resistance (Req) of the circuit for each of the three parallel circuits you tested.
6. Study the equivalent resistance readings for the parallel circuits. Devise a rule for the
equivalent resistance of a parallel circuit of two resistors.
7. Examine the results of Part II. What do you notice about the relationship between the three
voltage readings V1, V2, and VTOT in parallel circuits.
8. What did you discover about the current flow in a series circuit in Part III?
9. What did you discover about the current flow in a parallel circuit in Part III?
10. If the two measured currents in your parallel circuit were not the same, which resistor had the
larger current going through it? Why?
EXTENSIONS
1. Try this experiment using three resistors in parallel.
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Experiment 2-4
Capacitors
The charge q on a capacitor’s plate is proportional to the potential difference V across the
capacitor. We express this with
q
V 
C
where C is a proportionality constant known as the capacitance. C is measured in the unit of the
farad, F, (1 farad = 1 coulomb/volt).
If a capacitor of capacitance C (in farads), initially charged to a potential V0 (volts) is connected
across a resistor R (in ohms), a time-dependent current will flow according to Ohm’s law. This
situation is shown by the RC (resistor-capacitor) circuit below when the switch is closed.
Figure 1
As the current flows, the charge q is depleted, reducing the potential across the capacitor, which
in turn reduces the current. This process creates an exponentially decreasing current, modeled by
V (t )  V0 e
t
 RC
The rate of the decrease is determined by the product RC, known as the time constant of the
circuit. A large time constant means that the capacitor will discharge slowly.
OBJECTIVES
 Measure an experimental time constant of a resistor-capacitor circuit.
 Compare the time constant to the value predicted from the component values of the resistance
and capacitance.
 Measure the potential across a capacitor as a function of time as it discharges.
 Fit an exponential function to the data. One of the fit parameters corresponds to an
experimental time constant.
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Circuit Labs
MATERIALS
Vernier Circuit Board with batteries
4700 F capacitor
47 and 100 k resistors
2 D Batteries
Connecting wires
Voltmeter
External Circuit Board
PRELIMINARY QUESTIONS
1. Consider a candy jar, initially with 1000 candies. You walk past it once each hour. Since you
don’t want anyone to notice that you’re taking candy, each time you take just 10% of the
candies remaining in the jar. Sketch a graph of the number of candies remaining as a function
of time.
2. How would the graph change if instead of removing 10% of the candies, you removed 20%?
Sketch your new graph.
PROCEDURE
1. Connect the circuit with the 4700 F capacitor and the 47 k resistor in series but do not
make a complete circuit with the battery until you are ready to start timing in step 3. Record
the values of your resistor and capacitor in your data table, as well as any tolerance values
marked on them.
2. Connect the voltmeter across the resistor.
3. Monitor the input to determine the maximum voltage your battery produces.
a. Charge the capacitor with the switch in the position as illustrated in Figure 1.
b. Watch the reading on the voltmeter screen and note the maximum value reached. You will
need this value in a later step.
c. Record the voltage reading every 5 seconds as the capacitor charges.
d. Discontinue recording when the voltage reaches 0 or remains constant for 3 consecutive
periods.
4. Carefully disconnect the circuit, starting with the capacitor making sure that the capacitor is
not in a complete circuit loop.
5. Redesign the circuit with only the resistor and capacitor making a complete circuit. Be ready
to record voltages immediately on completing circuit.
6. Measure the voltage as the circuit discharges, record the initial value every 5 seconds until
the voltage reaches 0 or stays constant for 3 consecutive periods.
7. Repeat the experiment with the 100 k resistor in place of the 47 k resistor. How do you
think this change will affect the way the capacitor discharges? Rebuild your circuit using the
100 k resistor and repeat Steps 1-6.
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Experiment 2-4
ANALYSIS
1. In the data table, calculate the time constant of the circuit used; that is, the product of
resistance in ohms and capacitance in farads. (Note that 1 F = 1 s).
2. Next, fit the exponential function y = A e–B*x to your data.
a. Enter time in L1 and Voltage values for the 47 k resistor in L2 (charging data) and L3
(discharge data) and for the 100 k resistor in L4 (charging) and L5 (discharge)
b. Calculate y = A e–B*x for each list.
3. Print or sketch the graph of potential vs. time.
4
Compare the fit equation to the mathematical model for a capacitor discharge proposed in the
introduction,
V (t )  V0 e
t
 RC
5. Calculate a value t for each run and determine if it remains constant for the resistor.
EXTENSIONS
1. Instead of using a voltmeter in parallel attach an ammeter in series and measure current
change as you charge and discharge the capacitor with the 47 k resistor.
2. Instead of using meter place a light bulb in series with the capacitor and the 47 k resistor
and describe qualitatively what happens as the capacitor charges and discharges.
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