Laboratory 13
Ohm’s Law and Simple Circuits
I. Introduction
In this experiment you will study the current-to-voltage relationship for several circuit
components. Electric circuits typically consist of simple metallic conductors (wires) which join
together other individual circuit components. In 1827, Georg S. Ohm discovered the relationship
between the voltage, current, and resistance for a simple metal conductor:
If the temperature and other physical conditions of a metallic conductor are
unchanged, the ratio of the potential difference to the current [i.e., (ΔV)/I ] is
constant. This constant ratio is the resistance of the conductor.
This relationship, now called Ohm’s law, is often written in the form
ΔV = I R
[1],
where ΔV is the potential difference across the conductor, I is the current passing through the
conductor, and R is the resistance (always positive). The usual units of these quantities are listed
in Table 1. Materials that provide a very low resistance, such as copper and aluminum, we call
conductors; materials with a very high resistance, such as rubber and glass, are called insulators.
Resistors are electrical components whose resistance is somewhere in between. They are used to
control the flow of electricity through a circuit.
Table 1: Units of Ohm’s Law
Quantity
ΔV
I
R
Units
volts (V)
amperes (A)
ohms ()
Any electrical component, such as a resistor, gains energy when current flows through it.
The rate at which it gains energy is the power , P, delivered to the component, described by
P = I ΔV
[2]
For a resistor, the energy gained is thermal energy. Once the resistor reaches thermal equilibrium,
the power delivered equals the power emitted by the resistor, as heat or as light (in the case of a
glowing light bulb filament).
In the first part of this laboratory, we shall examine the current-voltage relationship for the
simplest circuit element, a piece of wire. In the second part, we will examine the resistance of a
light bulb and will use two light bulbs connected together to observe current flow in parallel and
series combinations.
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CAUTIONS
 You will be building circuits according to diagrams provided. Typically, circuit diagrams are
schematic, meaning they show how the pieces are connected logically, but not how they would
look in a photograph or ordinary drawing. See Figure 1 for examples of an ordinary drawing
and the equivalent schematic circuit diagram.
 You must verify each circuit you build before turning on the power supply. To do this, use
your finger to trace the current path in the actual wires from the point it leaves the power
supply (the red “+” terminal), through the wires and other components, and back to the black
“–” terminal of the power supply. As you trace the wires, compare to the circuit diagram.
 Make sure no metal parts are accidentally touching each other, as this could cause a short
circuit and damage the power supply. If at any point the power supply’s overload light comes
on, quickly turn off the power supply and examine the circuit.
 After you are finished with a circuit, turn down the knob on the power supply and switch it off.
II. Electrical Resistance of a Metal Wire
Electrical resistance can be determined by measurement of current and potential difference.
Set up the circuit shown in Figure 1, as described below. The current originates from the positive
(red) terminal on the DC power supply and flows clockwise through the circuit.
(1) Take one of the multimeters to use as an ammeter (current meter). Turn the multimeter knob
to the 10A setting. To connect things, you will use the provided wires, known as patch cords
(the thick red or black insulated wires with banana plug connectors at either end). Connect a
black patch cord wire to the COM port, and a red patch cord to the 10A port. Use other patch
cord wires as needed to complete a circuit so the current flows into the ammeter’s 10A port,
out of the COM port, then through the mounted 1-meter wire and back to the power supply’s
negative terminal.
–
wire B
+
I
1-meter
mounted
wire
A
I
(a) Circuit Drawing
(b) Circuit Diagram (schematic)
Figure 1
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About Meters
 Ammeters are always part of the active circuit, because the measured current flows through the
meter.
 Voltmeters are not part of the circuit itself, they measure potential difference, but no current
flows into or through the voltmeter (ideally!).
 Ohmmeters are never used on a circuit – only on a component removed from the circuit.
 Never change the meter dial while it is connected to a circuit!
(2) Turn on the power supply and adjust it so that the reading on the ammeter is about 0.50A.
(3) Take a second multimeter to use as a voltmeter, to measure potential
__
difference. Turn the multimeter knob to the V 
setting. Connect a
black wire to the COM port and a red wire to the V port. Press the
free end of the black wire firmly against the mounted wire at the 20cm
mark, simultaneously press the end of the red wire at the 70cm mark,
and note the reading.
NOTE: a positive number shown on the meter means that the red (V)
wire is at a higher potential than the black (COM) wire.
Q1: What is the potential difference, ΔV ? What happens to the reading if you swap the wire
ends? Which location (20 or 70cm) is at the higher potential? What do you calculate for the
resistance of this 50cm piece of wire?
(4) Now measure the potential difference between the 20cm mark and the 30cm mark.
Q2: What is the potential difference, ΔV ? What is the calculated resistance? Can you explain
how the resistance of this 10cm piece of wire relates to the resistance calculated in the
previous question?
Q3: Measure the potential difference between the ends of “Wire B”, (the one connecting the
power supply to the current meter). What do you calculate for the resistance of this wire?
Inside a uniformly conducting wire, there is a uniform electric field that pushes positive
charge from high potential toward low potential, and
Ex  
V
x
[3]
Q4: What is the size of the electric field in the 1-meter wire? (give units) What direction (left or
right) does the electric field point, and what is the direction of current flow?
(5) Now we will test Ohm’s Law. Because you will make several readings, instead of just
touching the voltmeter wires to the test points, push them into the banana-plug sockets
(through the side, or stacked, if necessary) at either end of the mounted 1-meter wire. Adjust
the current upwards in steps of about 0.1A, from 0.0 to 0.5A, recording the potential difference
ΔV across the wire each time. You do not need to set the current exactly (e.g., you can use
0.22A instead of 0.20A), but do record the exact actual reading of the current meter.
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(6) Make a plot of your data in Excel, with the Voltage data as y and the Current data as x. Add a
linear trend line with the intercept = 0 and have the equation displayed on the graph. You do
not need to print out the graph.
Q5: What is the equation, in terms of ΔV and I ? Are your data points consistent with a
proportional relationship? What is the resistance of the 1-meter wire?
Q6: How much power is delivered to the 1-meter wire at the 0.5A setting? Feel the wire after the
current has been flowing for a minute or so. Is it warm, compared to the adjacent metal
strip? Why is that?
(7) Shut off the power supply and disconnect all the wires to the 1-meter wire.
(8) You will measure the resistance directly, using a digital multimeter. Turn the multimeter knob
to the  setting. Connect a long black patch cord to the COM port, and red one to the V
port. Connect the free ends to either end of the 1-meter wire and record the resistance value.
Q7: Does the measured resistance agree with the resistance from the ΔV vs. I equation? What
happens to the reading if you swap the ends of the wire?
NOTE: Most metal wires have a very small resistance, but for this lab we have chosen a
special metal alloy with a larger resistance so that it can be easily measured.
tungsten
filament
III. Electrical Resistance of a Light Bulb
side
electode
For this section you will need the circuit board with three small light bulbs.
Each bulb contains a filament – a fine wire shaped into a tiny coil. One end of
the filament is attached to the bottom electrode of the bulb and the other end is
attached to the side electrode.
bottom
electode
(1) Measure & record the resistance R0 of one bulb using the digital multimeter (this can be done
most easily by leaving the bulb in the socket and measuring the resistance between the
connectors on each side).
(2) Construct the circuit as shown in Figure 2, using
one of the bulbs.
(3) Before turning on the power supply, dial down the
voltage all the way counter-clockwise. Turn on the
supply and slowly turn the control knob until the
supply panel meter shows about 4 or 5 Volts and
you see the bulb light up.
-
+
I
adjustable
power supply
red
10A port
ammeter A
2
black
COM port
1
Figure 2
(4) Take another multimeter and set it up as a voltmeter (see top of previous page). Measure the
potential difference between Point 1 and Point 2, ΔV1-2, which we will call simply ΔVbulb. Now
adjust the supply knob so that ΔVbulb ≈ 3 V. We will refer to this as the “low” setting for the
light bulb. Record the exact ΔVbulb and also the current measured by the ammeter.
(5) Raise the supply setting until ΔVbulb ≈ 6 V, which we will call the “high” setting. Again record
ΔVbulb and I.
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Q8: What do you calculate for the power delivered to the bulb at each of the two settings? How
does the power affect the brightness of the light bulb?
Q9: From your measurements, calculate the resistance R at the high and low settings. What
happens to the resistance of the light bulb as the power is increased?
Any metal component provides an electrical resistance. However, the resistance is
dependent on the crystalline structure, the physical geometry, and the temperature of the material.
The temperature dependence can be modeled as
R = R0[1 + α(T – T0)],
[4]
where R0 is the resistance at room temperature, T0 is the room temperature, and the temperature
coefficient α = 4.5×10–3 C–1 for tungsten.
Q10: Calculate the approximate temperature T of the bulb’s tungsten filament at both the low and
high power settings, using Eq. [4]. (Assume that T0 = 20°C.) Do the values seem
reasonable?
Sometimes, resistors are used in combination. Two ways resistors may be combined are in series
(Figure 3) and in parallel (Figure 4).
R1
R1
R2
R2
Figure 3: Resistors connected in series.
Figure 4: Resistors connected in parallel.
When two resistors are connected in series, the combination may be thought of as one larger
resistor. The resistance of this larger resistor can be determined by summing the two resistances,
Req = R1 + R2
[5a]
When two resistors are connected in parallel, current flows more easily, and the combination may
be thought of as one smaller resistor. The equivalent resistance of the combination is
1
1
1


Req R1 R2
[5b]
Light Bulbs in Series
We will now study resistors in series. Although we did not measure the resistance of the
other bulb, we will assume that the resistance properties of all the bulbs are nearly identical.
(6) Set up the circuit as shown in Figure 5 using two bulbs. To keep things comparable, we will
want the temperature of the bulbs to be the same as before, for the “low” setting. Measure
ΔVbulb for each bulb, and adjust the power supply so that each has ΔVbulb ≈ 3 V.
I
+
10A port
A
3
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COM port
1
Figure 5
5
(7) Now measure the potential difference ΔV1-3 across the entire series-double-bulb. Also record
the current.
Q11: Consider the series-double-bulb as one unit, and use your measurements to calculate the
power delivered to it and the resistance of it.
Q12: How does the resistance of this combination compare to the resistance of the single light
bulb (at the same temperature, “low” setting)? Explain, using the theory, previous page.
Q13: Taking care not to burn yourself, try unscrewing one of the bulbs. Why does the other bulb
go out? [Hint: watch the current meter.]
(8) Take one of the unused patch-cord wires. Touch one end of the wire to Point 1 and the other
end to Point 2. You have “short-circuited” one light bulb.
Q14: Why does the “shorted” bulb go out? Why does the other bulb get brighter? Explain.
Light Bulbs in Parallel
(9) We will now study the effects of resistors in parallel. Set up the circuit shown in Figure 6.
Adjust the power supply so that ΔVbulb ≈ 3 V. Record the current and voltage.
-
I
+
10A port
A
COM port
2
1
Figure 6
Q15: Again being careful not to burn yourself, try unscrewing one of the bulbs. What happens to
the other bulb? Explain why.
Q16: How does the resistance of this combination compare to the resistance of a single light bulb?
Does it agree with the prediction of Eq. [5b]? Show a calculation to support your answer.
Q17: How does the power delivered to this combination compare to the power to a single light
bulb at the low setting?
Q18: Based on your observations of series and parallel combinations, do you think the light bulbs
in your home are joined in series or parallel? Explain.
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Answer Sheet
Laboratory 13
Names: ___________________
___________________
II. Electrical Resistance of a Metal Wire
Q1:
Q2:
Q3:
Q4:
Current
Voltage
Q5:
Q6:
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Q7:
III. Electrical Resistance of a Light Bulb
bulb resistance R0
(multimeter)
measured V
measured current
low setting
high setting
Q8:
Q9:
Q10:
Light Bulbs in Series
measured V1-3
measured current
Q11:
Q12:
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Q13:
Q14:
Light Bulbs in Parallel
measured V
measured current
Q15:
Q16:
Q17:
Q18:
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