July 15, 2008 – DC Circuits and Ohm’s Law
1
Name ________________________ Date ____________ Partners_______________________________
DC CIRCUITS AND OHM'S LAW
AMPS
+
-
VOLTS
OBJECTIVES
•
To learn to apply the concept of potential difference
(voltage) to explain the action of a battery in a circuit.
•
To understand how potential difference (voltage) is
distributed in different parts of series and parallel circuits.
•
To understand the quantitative relationship between
potential difference and current for a resistor (Ohm's law).
•
To examine Kirchhoff’s circuit rules.
OVERVIEW
In a previous lab you explored currents at different points in
series and parallel circuits. You saw that in a series circuit, the
current is the same through all elements. You also saw that in
a parallel circuit, the sum of the currents entering a junction
equals the sum of the currents leaving the junction.
You have also observed that when two or more parallel
branches are connected directly across a battery, making a
change in one branch does not affect the current in the other
branch(es), while changing one part of a series circuit changes
the current in all parts of that series circuit.
In carrying out these observations of series and parallel circuits,
you have seen that connecting light bulbs in series results in a
larger resistance to current and therefore a smaller current,
while a parallel connection results in a smaller resistance and
larger current.
You will first examine the role of a battery in causing a current
in a circuit. You will then compare the potential differences
(voltages) across different parts of series and parallel circuits.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
2
July 15, 2008 – DC Circuits and Ohm’s Law
Based on your previous observations, you probably associate a
large resistance connected to a battery with a small current, and
a small resistance with a large current. You will explore the
quantitative relationship between the current through a resistor
and the potential difference (voltage) across the resistor. This
relationship is known as Ohm's law. You will then use
Kirchhoff's circuit rules to completely solve a DC circuit.
INVESTIGATION 1: BATTERIES AND VOLTAGES IN SERIES CIRCUITS
So far you have developed a current model and the concept of
resistance to explain the relative brightness of bulbs in simple
circuits. Your model says that when a battery is connected to a
complete circuit, there is a current. For a given battery, the
magnitude of the current depends on the total resistance of the
circuit. In this investigation you will explore batteries and the
potential differences (voltages) between various points in
circuits. In order to do this you will need the following items:
•
•
•
•
•
two voltage probes
two 1.5 volt D batteries (must be very fresh, alkaline)
and holders
six wires with alligator clip leads
two #14 bulbs in sockets
momentary contact switch
You have already seen what happens to the brightness of the
bulb in circuit 1-1a if you add a second bulb in series as shown
in circuit 1-1b. The two bulbs in Figure 1-1b are not as bright
as the original bulb. We concluded that the resistance of the
circuit is larger, resulting in less current through the bulbs.
B
A
C
Figure 1-1
Figure 1-1 shows series circuits with (a) one battery and one
bulb, (b) one battery and two bulbs and (c) two batteries and
two bulbs. (All batteries and all bulbs are assumed to be
identical.)
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
3
Prediction 1-1: What do you predict would happen to the
brightness of the bulbs if you connected a second battery in
series with the first at the same time you added the second
bulb, as in Figure 1-1c? How would the brightness of bulb A
in circuit 1-1a compare to bulb B in circuit 1-1c? To bulb C?
Do this before coming to lab.
ACTIVITY 1-1: BATTERY ACTION
1. Connect the circuit in Figure 1-1a, and observe the
brightness of the bulb.
2. Now connect the circuit in Figure 1-1c. [Be sure that the
batteries are connected in series – the positive terminal of
one must be connected to the negative terminal of the
other.]
Question 1-1: What do you conclude about the current in the
two bulb, two battery circuit as compared to the single bulb,
single battery circuit?
Prediction 1-2: Look carefully at the circuits in Figures 1-1a
and 1-2 (next page). What do you predict about the brightness
of bulb D in Figure 1-2 compared to bulb A in Figure 1-1a?
Do this before coming to lab.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
4
July 15, 2008 – DC Circuits and Ohm’s Law
D
Figure 1-2
3. Connect the circuit in Figure 1-2 (a series circuit with two
batteries and one bulb). Only close the switch for a
moment to observe the brightness of the bulb – otherwise,
you will burn out the bulb.
Question 1-2: How does increasing the number of batteries
connected in series affect the current in a series circuit?
When a battery is fresh, the voltage marked on it is actually a
measure of the emf (electromotive force) or electric potential
difference between its terminals. Voltage is an informal term
for emf or potential difference. We will use these three terms
(emf, potential difference, voltage) interchangeably.
Let's explore the potential differences of batteries and bulbs in
series and parallel circuits to see if we can come up with rules
for them as we did earlier for currents.
How do the potential differences of batteries add when the
batteries are connected in series or parallel? Figure 1-3 shows
a single battery, two batteries identical to it connected in series,
and two batteries identical to it connected in parallel.
Figure 1-3
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
5
Prediction 1-3: If the potential difference between points 1
and 2 in Figure 1-3a is known, predict the potential difference
between points 1 and 2 in Figure 1-3b (series connection) and
in Figure 1-3c (parallel connection). Do this before coming to
lab.
ACTIVITY 1-2: BATTERIES IN SERIES AND PARALLEL
You can measure potential differences with voltage probes
connected as shown in Figure 1-4.
+
+
A
+
-
VPA
+
B
+
-
VPB
-
-
+
+
+
+
-
A
VPA - +
-
B
VPB
VPA
-
(a)
+
A
-
+
- B
VPB
(c)
(b)
Figure 1-4
1. Open the experiment file L03.A1-2 Batteries.
2. Connect voltage probe VPA across a single battery (as in
Figure 1-4a), and voltage probe VPB across the other
identical battery. The red lead of the voltage probe goes to
the + side of the battery.
3. Record the voltage measured for each battery below:
Voltage of battery A: ___________
Voltage of battery B: ______________
4. Now connect the batteries in series as in Figure 1-4b, and
connect probe VPA to measure the potential difference
across battery A and probe VPB to measure the potential
difference across the series combination of the two
batteries. Record your measured values below.
Voltage of battery A: _____________
Voltage of A and B in series: _____________
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
6
July 15, 2008 – DC Circuits and Ohm’s Law
Question 1-3: Do your measured values approximately agree
with your predictions? If not, explain.
5. Now connect the batteries in parallel as in Figure 1-4c, and
connect probe VPA to measure the potential difference
across battery A and probe VPB to measure the potential
difference across the parallel combination of the two
batteries. Record your measured values below.
Voltage of battery A:____________
Voltage of A and B in parallel: ____________
Question 1-4: Do your measured values agree with your
predictions? Explain any differences.
Question 1-5: Write down a simple rule for finding the
combined voltage of a number of batteries that are
Connected in series:
Connected in parallel:
Do NOT do it, but consider what would happen if you wired two batteries
of unequal voltage in parallel, hook any two batteries together “antiparallel”, or simply short circuit” a single battery? To a very good
approximation, a real battery behaves as if it were an ideal battery in
series with a resistor. We speak of the battery having an internal
resistance. Since this “internal resistance” is usually quite small, the
voltages can cause a tremendous amount of current to flow which, in turn,
will cause the batteries to overheat (and possibly rupture).
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
7
You can now explore the potential difference across different
parts of a simple series circuit. Consider the circuit shown in
Figure 1-5.
S1
+
VPA
VP1
+
-
VPB
Figure 1-5
IMPORTANT NOTE: The switch (S1) should remain open except
when you are making a measurement. It is in the circuit to save the
battery. Use the momentary (push down) contact switch for S1.
Prediction 1-4: If bulbs A and B are identical, predict how the
potential difference (voltage) across bulb A in Figure 1-5 will
compare to the potential difference across the battery. How
about bulb B?
ACTIVITY 1-3: VOLTAGES IN SERIES CIRCUITS
1. Continue to use the experiment file L03.A1-2 Batteries.
2. Connect the voltage probes as in Figure 1-5 to measure the
potential difference across bulb A and across bulb B.
Record your measurements below.
Potential difference across bulb A: ______________
Potential difference across bulb B: ______________
Don’t be concerned if the bulb voltages are somewhat different,
because real bulbs do this. Ideal bulbs would have the same
voltage.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
8
July 15, 2008 – DC Circuits and Ohm’s Law
3. Now use one probe VPA to measure the voltage across both
bulbs A and B. Record your measurement below.
Potential difference across bulbs A and B: _____________
Question 1-6: Formulate a rule for how potential differences
across individual bulbs in a series connection combine to give
the total potential difference across the series combination of
the bulbs.
INVESTIGATION 2: VOLTAGES IN PARALLEL CIRCUITS
Now you will explore the potential differences across different
parts of a simple parallel circuit.
You will need the following material:
•
three voltage probes
• knife switch
•
1.5 V D cell battery (must be very fresh, alkaline) with
holder
•
two #14 bulbs with holders
•
momentary (push down) contact switch
• eight alligator clip leads
ACTIVITY 2-1: VOLTAGES IN A PARALLEL CIRCUIT
1. Open the experiment file L03.A2-1 Parallel Circuits,
which should show three voltage graphs as a function of
time.
2. Connect the circuit shown in Figure 2-1. Remember to use
the momentary contact switch for S1 and to leave it open
when you are not taking data.
Figure 2-1
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
9
3. Make sure both switches are open. Start taking data with
the computer. Leave both switches S1 and S2 open for a
couple of seconds. Then close switch S1 and after a second
or two, close switch S2. After another second or two stop
taking data and open both switches. Make sure you
remember what switches were open and closed on your
computer display showing both voltages. The voltage
probe connections as shown in Figure 2-1 will result in
positive voltages. The red lead is positive. If you measure
negative voltages, you probably have the leads switched.
4. Use the Smart Tool to make the following voltage
measurements of your data:
S1 open
S1 closed
S1 closed
S2 open
S2 open
S2 closed
Voltage across battery:
___________
___________
___________
Voltage across bulb A:
___________
___________
___________
Voltage across bulb B:
___________
___________
___________
5. Print out one set of graphs for your group.
Question 2-1: We have been led to believe that the voltage
across the battery would be constant. Yet when we close
switches S1 and S2 and draw current from the battery, we find
that the battery voltage changes. We say “We are placing a
load on the battery” or “We have a load on the battery”. Try to
explain what is happening in terms of the battery’s internal
resistance.
You have now observed that the voltage across a real battery
changes when we have a load on it (that is, drawing current
from the battery). An ideal battery would be one whose
voltage did not change at all, no matter how much current
flows through it. No battery is truly ideal (this is especially
true for a less than fresh battery), so the voltage usually drops
somewhat when the load on the battery is increased.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
10
July 15, 2008 – DC Circuits and Ohm’s Law
Because of this difficulty, we are now going to replace the
battery with an electronic power supply, which has been
designed to alleviate this problem. Keep your circuit as is.
ACTIVITY 2-2: VOLTAGES IN A PARALLEL CIRCUIT
We will replace the battery with an electronic power supply.
When you turn the dial, you change the voltage (potential
difference) between its terminals. The power supply we are
using can provide a constant voltage up to about 20 V
producing 1300 mA.
New equipment: HP6213A power supply.
1. Leave the power supply switch turned off except when
instructed to turn it on. Turn down the coarse adjustment
knob. Make sure the switch on the front is on VOLTAGE,
not CURRENT. Note that you will read the voltage on the
top (analog) scale of the meter. There are three inputs: +
(red), -, and ground
. We will use the + and – inputs.
2. Disconnect the two leads that now go to the battery and
connect the same two wires that went to + and – sides of the
battery to the + and – inputs of the power supply.
3. Open both switches S1 and S2 of your circuit.
4. Turn on the power supply and slowly turn up the coarse
knob to 2 V. Do not go over 2 V or you will burn out the
bulb. We will now repeat steps 3-5 of the previous activity.
5. Start taking data with the computer. Leave both switches
S1 and S2 open for a second or two. Then close switch S1
and after a second or two, close switch S2. After another
second or two stop taking data and open both switches.
Make sure you remember what switches were open and
closed on your computer display showing both voltages.
6. Use the Smart Tool to make the following voltage
measurements of your data:
S1 open
S1 closed
S1 closed
S2 open
S2 open
S2 closed
Voltage across battery:
___________
___________
___________
Voltage across bulb A:
___________
___________
___________
Voltage across bulb B:
___________
___________
___________
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
11
7. Print out one set of graphs for your group.
Question 2-2: Is the voltage across the power supply source
now constant as switches S1 and S2 are open or closed? Does
the power supply act as a constant EMF source?
Question 2-3: Are the voltages across both bulbs when the
two switches are closed similar to the voltage you measured
across the power supply? If not, explain.
Question 2-4: Based on your observations, formulate a rule
for the potential differences across the different branches of a
parallel circuit. How are these related to the voltage across the
power supply?
INVESTIGATION 3: OHM’S LAW
What is the relationship between current and potential
difference? You have already seen that there is only a potential
difference across a bulb or resistor when there is a current
through the circuit element. The next question is how does the
potential difference depend on the current? In order to explore
this, you will need the following:
•
•
•
current and voltage probes • #14 bulb in a socket
variable DC power supply
• ten alligator clip leads
10 Ω resistor (see prelab for color code)
Examine the circuit shown below, which allows you to measure
the current through the resistor when different voltages are
across it.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
12
July 15, 2008 – DC Circuits and Ohm’s Law
+ +
DC
Power
Supply
+
CPA
VPB
-
Figure 3-1
Prediction 3-1: What will happen to the current through the
resistor as you turn the dial on the power supply and increase
the applied voltage from zero? What about the voltage across
the resistor? Do this before coming to lab.
Ohm’s Law: The voltage, V, across an ideal resistor of
resistance R with a current I flowing through it is given by
Ohm’s Law:
V = IR
ACTIVITY 3-1: CURRENT AND POTENTIAL DIFFERENCE
FOR A RESISTOR
1. Open the experiment file L03.A3-1 Ohm’s Law.
2. Connect the circuit in Figure 3-1. The current probe goes
into analog port A, and the voltage probe into port B. Make
sure the power supply is turned off and the coarse
adjustment knob is turned down. Use a resistor of 10 Ω.
Note that the current probe is connected to measure the
current through the resistor, and the voltage probe is
connected to measure the potential difference across the
resistor.
3. Begin graphing current and voltage with the power supply
set to zero voltage, and watch your data as you slowly
increase the voltage to about 3 volts. Warning: Do not
exceed 3 volts! Stop the computer and turn the voltage
down to zero.
Question 3-1: What happened to the current in the circuit and
the voltage across the resistor as the power supply voltage was
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
13
increased?
Comment on the agreement between your
observations and your predictions.
4. If it’s not already visible, bring up the display for current
CPA versus voltage VPB. Notice that voltage is graphed on
the horizontal axis, since it is the independent variable in
our experiment.
5. Use the fit routine to verify that the relationship between
voltage and current for a resistor is a proportional one.
Record the slope.
Slope = _________________
Question 3-2: Determine the resistance R from the slope.
Show your work.
Calculated R = ________________
6. On the same graph, repeat steps 2 and 3 for a light bulb. Be
sure to increase the voltage very slowly for the light bulb,
especially in the beginning. Do not exceed 2.5 V or you
will burn out the bulb. There should now be two sets of
data on the I vs. V graph.
7. Print out one set of graphs for your group.
Question 3-3: Based on your data for the light bulb, does it
obey Ohm’s Law? Explain.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
14
July 15, 2008 – DC Circuits and Ohm’s Law
Question 3-4: If you were to repeat the previous measurement
with a 22 Ω resistor, describe the graph you would expect to
see compared with the 10 Ω resistor. How would the slope
differ?
INVESTIGATION 4: MEASURING CURRENT, VOLTAGE AND RESISTANCE
0.245
OFF ON
V
(a)
Ω
V, Ω COM
A
AC DC
(b)
A
A
V
Ω
20A
Figure 4-1
Figure 4-1a shows a multimeter with voltage, current and
resistance modes, and Figure 4-1b shows the symbols that will
be used to indicate these functions.
The multimeters available to you can be used to measure
current, voltage and resistance. All you need to do is choose
the correct dial setting, connect the wire leads to the correct
terminals on the meter and connect the meter correctly in the
circuit. Figure 4-1 shows a simplified diagram of a multimeter.
We will be using the multimeter to make DC (direct current)
measurements, so make sure the multimeter is set to DC mode.
A current probe or a multimeter used to measure current (an
ammeter) are both connected in a circuit in the same way.
Likewise, a voltage probe or a multimeter used to measure
voltage (a voltmeter) are both connected in a circuit in the same
way. The next two activities will remind you how to connect
them. The activities will also show you that when meters are
connected correctly, they don’t interfere with the currents or
voltages being measured.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
15
You will need:
• digital multimeter • current probe
• voltage probe
• power supply
• six alligator clip leads and wires
• 1000 Ω (1 %) , 10 Ω, 22 Ω and 75 Ω resistors (5%)
You found the color codes for these resistors in the prelab.
You should write the color codes down here:
10 Ω: _____________________________________________
22 Ω: _____________________________________________
75 Ω: _____________________________________________
1000 Ω: ___________________________________________
ACTIVITY 4-1: MEASURING CURRENT WITH A MULTIMETER
Figure 4-2
1. We want to measure the current in the circuit using the
multimeter in the current mode. We cannot use the current
probe we have been using, because they are not accurate at
low currents. Make sure the power supply is turned down
and turned off before beginning.
2. Set up the circuit shown in Figure 4-2. Replace the 10 Ω
resistor in the previous circuit with one having 1000 Ω.
3. Remove the current probe and insert the multimeter. In our
case the multimeter is being used in the ammeter mode.
The + side wire is connected to the mA port and the – side
wire to the COM port of the multimeter. Turn on the
power.
4. Set the multimeter to the 2 m (for 2 mA) scale on Current
to read the current.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
16
July 15, 2008 – DC Circuits and Ohm’s Law
5. Turn on the power supply and set the voltage to 2 V.
6. Open experimental file L03.A4-1 Multimeters.
Setup.
7. Click on Start and let it run for a few seconds.
Check
8. Read the current on the multimeter. If it reads negative,
you hooked the wires up backwards. You may need to
change multimeter scales to obtain a precise measurement.
Stop the computer. Write down the multimeter current and
determine the probe voltage.
Multimeter current: _______________
Computer voltage across resistor: _____________
9. Leave the coarse adjustment knob as it is on the power
supply, but turn off the power switch.
10. The 1000 Ω resistors are precise to 1% so we can determine
the current through them using Ohm’s law by dividing the
voltage across the resistor by the resistance value:
Calculate current I from Ohm’s law: _________________
Question 4-1: Compare the two currents determined in steps 8
and 10. Should they be the same? What is the percentage
difference?
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
17
Question 4-2: When used correctly as an ammeter, the
multimeter should measure the current through a resistor
without significantly affecting that current. Do we want the
ammeter to have a large or small resistor? What would be the
resistance of a perfect ammeter? Why? What happens to the
probe voltage you measure in the circuit if the ammeter is
removed? How do you explain this result?
ACTIVITY 4-2: MEASURING VOLTAGE WITH A MULTIMETER
Figure 4-3
Now we want to examine the use of a multimeter as a
voltmeter.
1. Set up the basic circuit in Figure 4-3 by connecting the
multimeter (in the voltmeter mode) across the resistor.
Note the + and – connections labeled on the figure. The
connections on the voltmeter will be between the sockets
labeled V (for +) and COM (for -). Set the multimeter scale
to measure 2 V (or 20 V if the voltage is greater than 2 V).
If the current is in the direction shown in Figure 4-3, then +
voltage will be measured. Otherwise, it will be - voltage.
Important: Use the volts setting and connect the leads to the
voltage terminals on the multimeter.
2. When ready, turn on the power supply, which should still
have the same setting as in the previous activity. Continue
to use the experimental file L03.A4-1 Multimeters.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
18
July 15, 2008 – DC Circuits and Ohm’s Law
3. Click on Start. Read the voltage on the multimeter and
write it down below. Stop taking data and turn off the
power supply.
4. Determine the probe voltage and write it down:
Multimeter voltage: _______________
Computer probe voltage: ____________
Question 4-3: Compare the two voltages measured here and in
step 8 of Activity 4-1. Should they all be the same? Explain
and discuss your results.
Question 4-4: When used correctly as a voltmeter, the
multimeter should measure the voltage across a resistor without
significantly affecting that voltage. How could you determine if
this voltmeter appears to behave as if it is a large or small
resistor? Describe your method and test it. Discuss your
results.
ACTIVITY 4-3: MEASURING RESISTANCE WITH A MULTIMETER
Next we will investigate how you measure resistance with a
multimeter. In earlier experiments, you may have observed
that light bulbs exhibit resistance that increases with the current
through the bulb (i.e. with the temperature of the filament). To
make the design and analysis of circuits as simple as possible,
it is desirable to have circuit elements with resistances that do
not change. For that reason, resistors are used in electric
circuits. The resistance of a well-designed resistor doesn't vary
with the amount of current passing through it (or with the
temperature), and they are inexpensive to manufacture.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
19
One type of resistor is a carbon resistor, and uses graphite
suspended in a hard glue binder. It is usually surrounded by a
plastic case. For several years resistors have had their value
identified with a color code painted on it. That is now slowly
changing to have the resistance value painted on it.
Cutaway view of a
carbon resistor showing
the cross sectional area
of the graphite material
Figure 4-4
The color code on our resistors tells you the value of the
resistance and the tolerance (guaranteed accuracy) of this value.
You did a prelab problem to help you learn this. We are using
four-band resistors in the lab. The first two stripes indicate the
two digits of the resistance value. The third stripe indicates the
power-of-ten multiplier.
The following key shows the corresponding values:
black = 0
brown = 1
red = 2
orange = 3
yellow = 4
green = 5
blue = 6
violet = 7
grey = 8
white = 9
The fourth stripe tells the tolerance according to the following
key:
red or none = ± 20%
silver = = ± 10%
gold = ± 5%
brown = ± 1%
As an example, look at the resistor in Figure 4-5. Its two digits
are 1 and 2 and the multiplier is 103, so its value is 12 x 103, or
12,000 Ω. The tolerance is ± 20%, so the value might actually
be as large as 14,400 Ω or as small as 9,600 Ω.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
20
July 15, 2008 – DC Circuits and Ohm’s Law
Orange
Brown
Red
None
Figure 4-5
The connection of the multimeter to measure resistance is
shown in Figure 4-6. When the multimeter is in its ohmmeter
mode, it connects a known voltage across the resistor, and
measures the current through the resistor. Then resistance is
determined by the multimeter from Ohm’s law.
Note:
Resistors must be isolated from the circuit by
disconnecting them before measuring their resistance. This also
prevents damage to the multimeter that may occur if a voltage is
connected across its leads while it is in the resistance mode.
Ω
Figure 4-6
1. Choose two different resistors other than 10 Ω and 1000 Ω
(call them R1 and R2). Write down the colors, resistances
and tolerances.
R1 color code: ___________________________________
R1: __________ Ω ± __________ %
R2 color code: ___________________________________
R2: ________ Ω ± ________ %
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
July 15, 2008 – DC Circuits and Ohm’s Law
21
2. Set up the multimeter as an ohmmeter and measure the
resistors:
R1: _____________ Ω
R2: _______________ Ω
Question 4-5: Comment on the agreement between the color
codes and the measurement. Are they consistent? Discuss.
3. Measure the resistance of the two resistors in series. Use
alligator clip wires to connect the resistors.
Rseries: __________ Ω
The equivalent resistance of a series circuit of two resistors (R1
and R2) of resistance R1 and R2 is given by:
Rseries = R1 + R2
Question 4-6: Calculate the equivalent series resistance and
compare with your measurement. Comment on the agreement.
The equivalent resistance of a parallel circuit of two resistors of
resistance R1 and R2 is given by:
1
R parallel
=
1 1
+
R1 R2
4. Measure the equivalent resistance of the two resistors in
parallel.
Rparallel: __________ Ω
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
22
July 15, 2008 – DC Circuits and Ohm’s Law
Question 4-7: Calculate the equivalent parallel resistance and
compare with your measurement. Comment on the agreement.
INVESTIGATION 5: COMPLEX CIRCUITS
We now want to combine series and parallel circuits into more
complicated circuits that are used in real electronics that affects
our everyday lives. We could use Kirchoff’s rules to determine
the currents in such complicated circuits, but now that we know
how to use multimeters, we will first simply study these
complex circuits.
We often want the ability to change the current in a circuit. We
can do that by adjusting the voltage in the power supply, or we
can change the resistor values. We shall first examine the use
of variable resistors, called potentiometers.
ACTIVITY 5-1: USING POTENTIOMETERS
In order to do the following activity you'll need a couple of
resistors and a multimeter as follows:
•
digital multimeter
•
200 Ω potentiometer
•
a few alligator clip lead wires
Figure 5-1
A potentiometer (shown schematically in Figure 5-1) is a
variable resistor. It is a strip of resistive material with leads at
each end and another lead connected to a “wiper” (moved by a
dial) that makes contact with the strip. As the dial is rotated,
the amount of resistive material between terminals 1 and 2, and
between 2 and 3, changes. When turning knobs on most
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
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July 15, 2008 – DC Circuits and Ohm’s Law
23
electrical items, you are
potentiometer like this one.
actually
usually
turning
a
1. Use the resistance mode of the multimeter to measure the
resistance between the center lead on the variable resistor
and one of the other leads.
Question 5-1: What happens to the resistance reading as you
rotate the dial on the variable resistor clockwise?
Counterclockwise?
2. Set the variable resistor so that there is 100 Ω between the
center lead and one of the other leads.
ACTIVITY 5-2: PREPARE CIRCUIT
You will set up the circuit below in Figure 5-2 such that 50 mA
will pass through the ammeter (multimeter). Use the power
supply for the source of voltage.
2 V+
R
–
A
2
R3
R1
Figure 5-2
1. You are given two resistors in addition to the potentiometer:
22 Ω and 1000 Ω. The potentiometer must be used in the R3
position, but the other two resistors may be placed in either
R1 or R2 as you find necessary.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
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24
July 15, 2008 – DC Circuits and Ohm’s Law
2. Set the power supply to about 2 V by using the power supply
meter scale. The precise value is not important. You are not
allowed to change the voltage after initially setting it.
3. You are to determine the positions of the two resistors and
adjust the potentiometer to obtain a current of 50 mA in the
ammeter (multimeter).
R1 (circle value):
22 Ω
1000 Ω
R2 (circle value):
22 Ω
1000 Ω
4. Show your TA when you are finished.
TA initials: ____________________________
ACTIVITY 5-3: KIRCHHOFF’S CIRCUIT RULES
Suppose you want to calculate the currents in various branches
of a circuit that has many components wired together in a
complex array. The rules for combining resistors are very
convenient in circuits made up only of resistors that are
connected in series or parallel. But, while it may be possible in
some cases to simplify parts of a circuit with the series and
parallel rules, complete simplification to an equivalent
resistance is often impossible, especially when components
other than resistors are included.
The application of
Kirchhoff’s Circuit Rules can help you to understand the most
complex circuits.
Before summarizing these rules, we need to define the terms
junction and branch. Figure 5-3 illustrates the definitions of
these two terms for an arbitrary circuit.
A junction in a circuit is a place where two or more circuit
elements are connected together.
A branch is a portion of the circuit in which the current is the
same through every circuit element. [That is, the circuit
elements within the branch are all connected in series with each
other.]
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
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July 15, 2008 – DC Circuits and Ohm’s Law
25
Junction 1
4Ω
12 V
+
6Ω
–
6V
+
4V
Branch 1
4Ω
R
+
–
+
12 V
Branch 2
4V
–
+
6Ω
–
Branch 3
R
6V
+
–
–
Junction 2
(b)
(a)
Figure 5-3
Kirchhoff’s rules can be summarized as follows:
1. Junction Rule (based on charge conservation): The sum of
all the currents entering any junction of the circuit must
equal the sum of the currents leaving.
2. Loop Rule (based on energy conservation): Around any
closed loop in a circuit, the sum of all changes in potential
(emfs and potential drops across resistors and other circuit
elements) must equal zero.
You have probably already learned how to apply Kirchhoff’s
rules in lecture, but if not, here is a quick summary:
1. Assign a current symbol to each branch of the circuit, and
label the current in each branch (I1, I2, I3, etc.).
2. Assign a direction to each current. The direction chosen for
the current in each branch is arbitrary. If you chose the
right direction, the current will come out positive. If you
chose the wrong direction, the current will eventually come
out negative, indicating that you originally chose the wrong
direction.
Remember that the current is the same
everywhere in a branch.
3. Apply the Loop Rule to each of the loops.
(a) Let the voltage drop across each resistor be the product of
the resistance and the net current through the resistor
(Ohm’s Law). Remember to make the sign negative if you
are traversing a resistor in the direction of the current and
positive if you are traversing the resistor in the direction
opposite to that of the current.
(b) Assign a positive potential difference when the loop
traverses from the “–” to the “+” terminal of a battery. If
you are going across a battery in the opposite direction,
assign a negative potential difference.
4. Find each of the junctions and apply the Junction Rule to it.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
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July 15, 2008 – DC Circuits and Ohm’s Law
Arbitrarily assigned loop
direction for keeping
track of currents and
potential differences.
Junction 1
Current direction
through battery often
chosen as in direction
of – to +
I2
I1
ε1
+
–
Loop 1
I3
+
ε2
–
R3 Loop 2
I1
I2
R1
Junction 2
R2
Figure 5-4.
Now we’ll look at an example. In Figure 5-4 the directions for
the loops through the circuits and for the three currents are
assigned arbitrarily. If we assume that the internal resistances
of the batteries are negligible (i.e. that the batteries are ideal),
then by applying the Loop Rule we find that
Loop 1
Loop 2
ε 1 − I 3 R3 − I1R1 = 0
ε 2 − I 3 R3 − I 2 R2 = 0
(1)
(2)
By applying the Junction Rule to junction 1 (or 2), we find that
I1 + I 2 = I 3
(3)
It may trouble you that the current directions and directions that
the loops are traversed have been chosen arbitrarily. You can
explore this issue by changing these choices, and analyzing the
circuit again. You’ll find (assuming no algebraic errors, of
course) that you get the same answers.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
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July 15, 2008 – DC Circuits and Ohm’s Law
27
Prediction 5-1: Do this before coming to lab. Solve
Equations 1 through 3 for the currents I1 , I 2 and I 3 in terms of
the resistances R1 , R2 and R3 and the emfs ε 1 and ε 2 . Write
your results for the three currents below using symbols.
You will use these results in the prelab homework to calculate
the currents. The resistances will be given to you in your prelab
homework and will be similar to, but not exactly, the same as
R1 = 75 Ω, R2 = 10 Ω, and R3 = 39 Ω. Use ε 1 = 6.0 V, ε 2 = 1.5
V. Then write numerical values of the three currents below
using the resistance values determined in the prelab homework.
I1: _________________________
I2: _________________________
I3: _________________________
ACTIVITY 5-3: TESTING KIRCHHOFF’S RULES WITH A REAL
CIRCUIT
In order to do the following activity you'll need a couple of
resistors and a multimeter as follows:
•
three resistors (10 Ω, 39 Ω and 75 Ω, all 5%)
•
digital multimeter
•
DC power supply
•
1.5 V D battery (very fresh, alkaline) and holder
•
eight alligator clip lead wires
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
28
July 15, 2008 – DC Circuits and Ohm’s Law
1. You have previously measured the values of the three
resistors in Investigation 4 or you can easily measure them
again with the multimeter. Set the power supply voltage to
6.0 V and measure the voltage of the 1.5 V battery with
your multimeter. Record all the results below.
Measured voltage (emf) of power supply
ε 1 :_______
Measured voltage (emf) of the 1.5 V battery ε 2 :_______
Measured resistance of the 75 Ω resistor
R1 :_______
Measured resistance of the 10 Ω resistor
R2 :_______
Measured resistance of the 39 Ω resistor
R3 :_______
2. Wire up the circuit pictured in Figure 5-4. Spread the wires
and circuit elements out on the table so that the circuit
looks as much like Figure 5-4 as possible. [It will be a big
mess!]
Note: The most accurate and easiest way to measure the
currents with the digital multimeter is to measure the voltage
across a resistor of known value, and then use Ohm's Law to
calculate I from the measured V and R.
Pay careful attention to the “+” and “-” connections of the
voltmeter, so that you are checking not only the magnitude of
the current, but also its direction.
3. Use the multimeter to measure the voltage drops across the
resistors and enter your data in Table 5-1 (don’t forget to
use appropriate units!). Fill in the rest of the table:
Calculate the corresponding currents and the percent
difference between these values and those of the pre-lab.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
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July 15, 2008 – DC Circuits and Ohm’s Law
29
Table 5-1 Results from Test of Kirchhoff's Circuit Rules
Rnominal
I nominal
(prelab)
(prelab)
Rmeasured
Vmeasured
I determined
% Difference
I nominal , I determined
R1
R2
R3
Question 5-2: Discuss how well your measured currents agree
with the pre-lab nominal values and consider possible sources
of error. Were the directions of the currents confirmed?
Question 5-3: What characteristic(s) of real batteries would
lead us to expect that your experimentally determined currents
would be less than predicted? Discuss.
Question 5-4: Explain how using 1% resistors might result in
the differences in the last column above (between the nominal
and determined values of current) to be smaller.
University of Virginia Physics Department
PHYS 636, Summer 2008
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000
30
University of Virginia Physics Department
PHYS 636, Summer 2008
July 15, 2008 – DC Circuits and Ohm’s Law
Modified from P. Laws, D. Sokoloff, R. Thornton
Supported by National Science Foundation
and the U.S. Dept. of Education, 1993-2000