Download Resistance in series and parallel

PHYSICS 125 LAB 5: RESISTANCES IN SERIES AND PARALLEL
Goal:
This lab will investigate the relationship between the current and voltage for resistors in series or
in parallel. We will also see that these combinations of resistors are equivalent to a single
equivalent resistance. This lab also reinforces our understanding of current flow in a circuit and
helps clarify the meaning of potential differences in series combinations.
Background reading:
Review section 18.1 (Resistances in Series, Parallel, and Series-Parallel Combinations).
Equipment needed:
DC power supply
Connecting wires (with banana plugs, on wall rack)
DPDT switch (with spade lugs to banana adapters)
2 Digital multimeters (Fluke D810 or equivalent)
Resistors (10, 15, and 25 ohm)
Theory:
As described in your textbook, a combination of resistors in series is equivalent to a single
resistor of resistance value Rs = R1 + R2 + R3. The current that flows through each of the
resistors in the series combination is the same. In a parallel combination, the current is divided
into several branches, but the voltage is the same across each resistor. Consequently, the
equivalent resistance for resistors in parallel is 1/Rp = 1/R1 + 1/R2 + 1/R3. (Of course, these
formulae are for three resistors and have to be modified for a different number of resistors.)
Experimental Procedure:
1. We will set up the circuits shown in the diagrams, using 10, 15, and 25  resistors. Before
you actually set up the circuit, record the values of the resistors, as printed on the resistors, in the
table in the lab report. These are called “nominal” values. The manufacturing process cannot
produce exact values, so the actual value of the resistance will vary slightly from the nominal
value. To measure this, use one of the DMMs, with the switches set for DC, /S, 200  , and
plug the connecting wires (probes) into the COMMON and  inputs. Measure the resistance of
each resistor and record the measured values on the lab report.
Now set up the first circuit as shown on the next page. One of the DMMs will be used as
an ammeter to measure current through the resistors, and should be set for DC, mA/A, 2000mA
with the pushbuttons, and the connecting wires should be plugged into the COMMON and the
mA inputs. The other DMM will be used as a voltmeter to measure the voltage across the series
combination or across each resistor, with the pushbuttons set for DC, V, and 20V, and the
connecting wires should be plugged into the COMMON and the V inputs. In the diagram, the
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arrows on the wires from the voltmeter indicate that it will be connected to the nodes just below
the tip of the arrow (i.e., the two ends of the resistor) and then it can be disconnected and
reconnected to measure the voltage across another resistor, for example R1, then R2, then R3.
Since you only have one ammeter, set it up in the left-most position in the circuit diagram. The
details of this procedure will be explained by the instructor.
Have your instructor check the circuit after you set it up, and before proceeding to turn on
any power. Leave the switch open to start with.
V
Switch
Power
Supply
A
A
A
R1
R2
R3
A
Resistors in series
2. After the instructor has checked the setup, turn the voltage knob on the power supply fully
counterclockwise, which will reduce the voltage to zero. Then close the switch and slowly turn
up the voltage until a voltage of approximately 5 V is indicated on the voltmeter. Observe the
current on the ammeter. Record the measured voltage (which might be different from 5.00 V)
and the measured current in the lab report. Open the switch when you are finished with these
measurements. This will prevent the resistors from getting too hot, due to the power dissipated
in the resistor (this would be P = I V). Sometimes these resistors get too hot to touch, depending
on the voltage, current, and the time that current flows through them.
3. To analyze this series resistor combination, calculate the equivalent resistance using the
nominal values of resistance of the three resistors. Then using the measured voltage, calculate
the current in this series combination and compare it with the measured current. Finally, use the
measured current to calculate the voltage drop across each of the resistors in the series and record
these estimated voltage drops in the lab report.
4. Now returning to the circuit, move the ammeter to the position between the first and second
resistor, close the switch, and record the current. To move the ammeter, it is usually best to
completely disconnect it from the circuit, and then put a wire in the place where the ammeter was
previously located. Then, break the circuit where you want to measure the current, and connect
the two wires from the ammeter to the two sides of the “break”. (This is usually a little tricky to
do the first time, so ask your instructor to check that you did it correctly.) After recording this
current, open the switch, and move the ammeter to the position between the second and third
resistor. Close the switch and record the current. Open the switch. The currents you measure
should be the same (or very close). Why is this true for the series circuit?
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5. Now remove the ammeter completely from the circuit, and use the voltmeter to measure the
voltage drop across each of the resistors, one at a time. Compare these readings with your
estimated voltages based on the previously measured current and the individual resistances.
Switch
Power
Supply
A
V
R2
R1
A
A
R3
A
Resistors in parallel
6. Now we will measure currents and voltages for resistors in parallel. Set up the circuit shown
in the figure. If you use the same resistors as in the series case, you can just record the same
nominal and measured values in the table on the lab report. Again, since you only have one
ammeter, put it in the top-most position shown in the diagram. You will measure the three
currents in the individual resistors in the next step. Measure the voltage across the parallel
combination, and the current which comes out of the power supply, for a voltage of 3 V
(nominal) on the power supply meter. Use the exact measured voltage, though, for the remaining
calculations. Open the switch. On paper, compute the equivalent resistance for the circuit. Then
calculate the total current that you would expect and compare with the measured current.
7. Returning to the experimental setup, close the switch and measure the voltage drops across
each resistor and across the parallel combination. You should get the same (or close to the same)
voltage. Then open the switch and move the ammeter in order to measure the current that flows
through resistor R1, close the switch and record the current. Repeat the current measurement for
resistor R2 and for resistor R3. Open the switch, and then compare your measured currents with a
theoretical prediction which can be made by using the voltage across each resistor, divided by
the nominal resistance of that resistor.
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PHYSICS 125 LAB REPORT:
Name__________________________________
RESISTANCES IN SERIES AND PARALLEL
Resistors in series
Resistor values (nominal)
R1 ____________
R2 ____________
R3
____________
Resistor values (measured)
R1 ____________
R2 ____________
R3
____________
Equivalent resistance (use measured values)
Rs = R1 + R2 + R3
Source voltage across combination
Calculated current in series
Vsource
I = Vsource / Rs
Measured current in series
Measurement for
Resistor
I
_____________
_____________
_____________
_____________
Measured
Voltage (Volts)
Measured
Current (Amps)
Measured
Resistance (
Calculated
Voltage (Volts)
1
V1
I1
R1
I1R1
2
V2
I2
R2
I2R2
3
V3
I3
R3
I3R3
Sum of measured voltages across resistors:
Vtotal = V1 + V2 + V3 =
_________________
Compare this to the Source voltage Vsource =
_________________
Compare the column of measured voltages to the column of calculated voltages.
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Resistors in parallel
Resistor values (nominal)
R1 ____________
R2 ____________
R3
____________
Resistor values (measured)
R1 ____________
R2 ____________
R3
____________
Equivalent resistance (use measured values) Rp = 1/(1/R1 + 1/R2 + 1/R3 )
Source voltage across combination
Vsource
Calculated current in combination
_____________
I = Vsource / Rp
_____________
Itotal
_____________
Measured total current in combination
Measurement for
Resistor
____________
Measured
Voltage (Volts)
Measured
Current (Amps)
Measured
Resistance (
Calculated
Voltage (Volts)
1
V1
I1
R1
I1R1
2
V2
I2
R2
I2R2
3
V3
I3
R3
I3R3
Compare the column of measured voltages to the column of calculated voltages.
(They should all be the same.)
Sum of measured currents through resistors:
Itotal = I1 + I2 + I3 =
Compare to the total current in the combination
Itotal
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_____________
_____________