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P27
RESISTORS IN SERIES AND IN PARALLEL
OBJECTIVE
The object of this experiment is to study the relationship between resistance, voltage, and
current in circuits containing resistors in series and in parallel.
THEORY
V
-
V1
R1
I
1
+
V2
+
R2
I
I
V3
+
2
R3
I
+
3
Figure 1
Resistors are said to be connected in series when they are joined as in Figure 1 so that the
same current I flows through each resistor. For a circuit containing resistors in series the
following statements are true:
1. The current in each part of the circuit is the same:
I = I1 = I2 = I3
2. The voltage across the group of resistors in series is equal to the sum of the voltages
across the individual resistors:
V = V1 + V2 + V3
3. The total resistance of the series group is equal to the sum of the individual resistances:
R = R1 + R 2 + R3
1
V
-
I
+
R1
+
R2
+
R3
+
I
I
1
2
I
3
Figure 2
When the resistors are arranged as in Figure 2 the total current I divides and part flows
through each resistor. An arrangement where the respective ends of several resistors are
connected to a common point is called a parallel arrangement. For a circuit containing
resistors in parallel, the following statements are true.
4. The total current is the sum of the separate currents:
I = I1 + I2 + I3
5. The voltage across each resistor is the same and is equal to the voltage across the entire
group:
V = V1 = V2 = V3
6. The reciprocal of the equivalent resistance of the group is equal to the sum of the
reciprocals of the separate resistances:
1
1
1
1
R = R1 + R2 + R3
The six statements above are studied in this experiment.
APPARATUS
Power supply set at 2.8 V DC; 0.5 amp ammeter; 3 volt voltmeter; 3 plug type resistance
boxes with 0.5 ohm coils; 2 four-way connectors; connecting leads.
2
PROCEDURE
Part 1. Resistors in Series
1. Connect three resistance boxes in series as shown in Figure 3. Use resistance values of
R1 = 2 ohms, R2 = 4 ohms, R3 = 6 ohms. To set R1 to 2 ohms, remove the plug labeled 2
while making sure that all the other plugs are in place and tight. Connect the ammeter
in position A1 initially. Remember that conventional current flowing in the (+)
ammeter terminal will give a right deflection of the meter hand. If you hook the
ammeter up backward the needle will try to deflect to the left but since there is a stop
on the left it can't. After wiring Figure 3, ask the instructor to check your wiring before
you plug the circuit into the power supply.
+
-
A4
R1
A3
+
R2
+
+
A1
+
A2
R3
Figure 3
2. Measure the current at positions A1 , A2 , A3 , and A4 as indicated in Figure 3.
3. Using the voltmeter, measure the voltage across each resistor, and then the voltage
across the entire group of resistors as indicated in Figure 4.
-
+
V4
R1
+
R2
V1
V2
+
Figure 4
3
R3
+
V3
+
Does the sum of V1 + V2 + V3 equal V4?
Part 2. Resistors in Parallel
Change the values of the three resistance boxes so that R1 = 10 ohms, R2 = 20 ohms, and R3
= 30 ohms. Connect the three resistance boxes in parallel as illustrated in Figure 5. Use the
two four-way connectors at A and B. Connect this arrangement to the battery through an
ammeter in position A4 .
V
-
+
R1
A
R2
R3
+
A1
+
A2
+
A3
+
A4
B
Figure 5
Leave one of the power supply terminals disconnected until the instructor checks the
wiring. Record the current I4 as indicated by the ammeter in position A4 . Break the
connection from the resistor R1 to the four-way connector B and insert the ammeter in
series with the resistor. This is position A1 of figure 5. Record this current as I1. Similarly
measure the currents I2 and I3 flowing through R2 and R3. Show from the observed data
that the individual currents vary inversely with the corresponding resistances; for example,
since
IR = I1R1 = I2R2 = I3R3
it follows that
I1
R2
=
I2
R1
I2
R3
and I = R
3
2
I1
R2
I2
R3
Note the percentage difference between the ratios I and R ; also between I and R .
2
1
3
2
4
Now remove resistance boxes R1 and R2. With the ammeter in position A3 of figure 5,
adjust the value of R3 until the current flow is as close as possible to that obtained for I4
earlier. Compare this resistance (Req measured) with that calculated using the reciprocal
law and values of R1 = 10 ohms, R2 = 20 ohms, R3 = 30 ohms. Record the percentage
difference.
Part 3. Resistors in Series - Parallel Combination
Connect the three resistance boxes as shown in Figure 6. Set R1 = 2.5 ohms, R2 = 4 ohms,
and R3 = 8 ohms. Use the four-way connectors at B and C.
V
-
+
R2
A
R1
B
C
R3
Figure 6
Measure the voltage across AC. (Do not measure any other voltages or currents.) Using
the voltage across AC and the values of the resistances R1 , R2 , and R3 calculate the
currents in each resistor. Finally measure each of these currents with the ammeter and
compare the calculated and measured values.
QUESTIONS:
1. Does the insertion of an ammeter into a circuit to measure the current in that circuit
affect the value of the current to be measured? Is it necessary for an ammeter to have a
low resistance or a high resistance? Explain.
2. Does the insertion of a voltmeter into a circuit to measure the voltage across a resistor,
as in Figure 4, change the voltage across that resistor? Is it desirable for voltmeter to
have a high resistance or a low resistance? State the reasons.
3. A string of Christmas tree lights is frequently made of miniature lamps connected in
series. For an 8-light, 120 Volt set, what is the voltage across each light? If one light
were removed, what would happen? The voltage across the empty socket becomes
equal to the line voltage. Why is this?
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4. A group of three resistors in parallel is connected in series with a 3.00 ohm resistor and
a battery of negligible internal resistance. The parallel group has resistances of 5.00,
8.00, and 12.0 ohms, respectively. If there is a current of 0.50 amp in the 12 ohm
resistor, what must be the emf of the battery?
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RESULTS
NAME
DATE
COURSE#
Part 1. Resistors in series.
I1
I2
V1
V2
I3
I4
V3
V4
V1 + V2 + V3
V4
=
=
Part 2. Resistors in parallel
I1
I2
I3
I4
R1
I1
I2
R2
R1
I2
I3
R3
R2
=
% difference
=
=
% difference
=
R2 _________
R3
Req calculated
Req measured
% difference
Note: Req is the single resistance which will result in the same I4 as the parallel
combination of R1, R2, and R3.
Show calculations:
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RESULTS - Page 2
NAME
DATE
COURSE#
Part 3. Resistors in Series - Parallel Combination
R1
VAC
R2
R3
Measured
Calculated
% Error
I1
I1
I1
I2
I2
I2
I3
I3
I3
Show calculations:
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P27
PRE-LAB
NAME
DATE
COURSE#
Calculate the current through resistor R1 below.
6V
R2
R1
R3
R1 = 8 Ω
R2 = 6 Ω
R3 = 12 Ω
I1 =
9