Experiment 7
Resistors
Preparation
Prepare for this week's experiment by reading about resistors and current in circuits, resistors in
series and parallel, Ohm's Law and Kirchhoff's Laws.
Principles
If you apply an electric field across a conductor there will be a potential difference between the
ends and current will flow. The current, I, is considered to be made up of positive charge
carriers moving through the conductor
I=
dq
.
dt
Charge carriers in a circuit gain energy from an emf source such as a battery and lose energy as
they move through resistors. The gain or loss of energy per unit charge is the voltage rise or
drop across the source or resistor.
Ohm's Law is an empirical relationship, not a fundamental law such as Newton's Laws, and is
generally written as
∆V
.
I=
R
Kirchhoff's Rules
1. The Junction Rule: The sum of the currents entering a junction must equal the sum of the
currents exiting the junction. Current is simply moving charges. The charges are not created or
destroyed in the circuit, nor can they leak out.
∑I
in
=
∑I
out
.
2. The Loop Rule: The sum of the potential changes around a closed loop in a circuit must
equal zero. Another way of saying this is that the sum of the voltage (or potential) rises from
emf sources must equal the sum of the voltage drops across the resistors.
∑
∆V = 0 .
closed
loop
In this experiment you will measure the voltage rises and drops across resistors and emf sources,
resistance, and current and use the data to confirm Ohm's Law and Kirchhoff's Rules.
If two resistors are wired in series the current through them must be the same. This is a
consequence of the junction rule. If the resistors do not have the same resistance, the voltage
drops across them will be different, in accordance with Ohm's Law. The consequence of this is
that the net or equivalent resistance of N resistors in series is found using
N
Req = ∑ Ri .
i=1
If two resistors are wired in parallel the voltage drops across them must be equal in accordance
with the loop rule. However, if the resistances are different the currents through them will be
different. The sum of their currents will follow the junction rule. The equivalent resistance of N
resistors in parallel is given by
N
1
1
=∑ .
Req
i=1 Ri
You will verify these equations using your data.
Equipment
1
1
1
1
1
1
1
1
2
3
3
powered protoboard
voltmeter
red and black test leads
red and black alligator clips for the test leads
330 Ω resistor
1 kΩ resistor
2 kΩ resistor
resistor substitution box
spade lugs
18" banana wires
small wires
Procedure
You will use the multimeter to measure three different quantities in this experiment. Measure
the resistance of a resistor by clipping the leads across it and setting the meter to "Ohms" Make
sure that there is no voltage across the resistor as you measure the resistance.
Measure voltage by placing the meter leads in parallel with the resistor or power supply. This
does not require any circuit rewiring.
Measure current by placing the meter in series with the circuit. This means that you must
interrupt the circuit and force all the current through the meter. If you do this incorrectly you
will blow the fuse in your meter.
1.
Use the chart at the front of the experiment to select a
330 Ω , a 1 kΩ , and a 2 kΩ resistor. Call these resistors
R1, R2, and R3. It does not matter which is which, but you
must be consistent and keep track of your resistor values
throughout the experiment or your data will be worthless.
2.
The marked resistor values are approximate. Use the multimeter (DMM) to determine the
actual resistance of each resistor.
3.
Build the circuit shown in Figure 1 and measure the voltage
across the power supply and each of the resistors.
4.
Measure the current at points A1, A2, and A3.
5.
Build the circuit shown in Figure 2. Measure the power
supply voltage. Measure the current at points A1, A2,
and A3.
Figure 1.
Figure 2.
6.
Wire the circuit shown in Figure 3. Measure the voltage across each power supply and
resistor.
7.
Set the resistor substitution box to the
equivalent resistance of R1 and R2 for the
series circuit. Measure the resistance of the
box, adjust it if necessary, and connect it in
series with the power supply and measure
the equivalent current, Ieq.
Figure 3.
8.
Set the resistor box to the equivalent resistance of R1 and R2 in
parallel and repeat the procedure.
9.
Turn everything off and put everything away. Be sure that you put the resistors away
properly.
Data
Data for the first circuit should consist of the resistor values, the power supply voltage, the
voltage across each resistor, and the three current measurements.
Data for the second circuit should consist of the resistor values, the power supply voltage, the
current through the circuit and the current through each resistor.
Data for the third circuit should consist of the resistor values, the power supply voltages and the
voltage across each resistor.
You should also have the equivalent resistance and the equivalent current for the series and
parallel circuit.
Analysis
Use the measured values in all your calculations. The unit for currents should be mA. Present
your results in tables as much as possible.
1.
For the series circuit calculate the current you would expect through each resistor based on
the voltage and resistor values. Compare these to the measured current. Was the current
the same throughout the circuit? Which laws have you verified?
2.
For the series circuit add the voltage drops across the resistors and compare the sum to the
power supply voltage. Which law does this verify?
3.
For the parallel circuit again calculate the predicted currents and compare them to the
measured values. Did the current through the two branches add up to the total current for
the circuit? Which law does this verify?
4.
For the combination circuit calculate the expected current through each resistor using
Ohm's Law. Do the currents through each loop add up properly? What law does this
verify?
5.
Compare the equivalent currents to the measured currents for the first two circuits. Which
law does this confirm?
Questions
1.
Draw neat schematics (using a ruler) of the three circuits used in this experiment. Label the
points at which you will make measurements and indicate what kind of measurements they
are. Show the meter polarity (where the positive and negative meter leads were used) for
all measurements.
2.
Derive the equations for the equivalent resistance of resistors in parallel and in series.
What happens to the current as more resistors are added to a series circuit? to a parallel
circuit?
3.
Use Kirchhoff's laws to set up three simultaneous equations that can be solved for the value
of each of the currents in Figure 3 in terms of the power supply voltages and the resistor
values. Use the measured resistor and power supply voltage values to calculate the
expected currents for the third circuit using the equations you derived. Compare the
theoretical and experimental results.
4.
Explain how a fuse works. Why is it extremely dangerous to put a too large a fuse in a
circuit?
If it applies to you, write "I have not cheated on this lab report" and sign your name.
Grading
4 pts
4 pts
Data and Analysis.
For each question.