Characteristics of Series and Parallel Circuits
In this laboratory exercise you will measure the characteristic voltages and currents in series, parallel, and
mixed series-parallel circuits. You will compare your experimental results with the formulas and principles
that govern those circuits.
1.
You will be using three resistors whose marked values are: 𝑅1 = 220 Ω, 𝑅2 = 330 Ω, and
𝑅3 = 470 Ω. Use your multimeter to measure the resistance of each of these resistors. Note
units carefully, and write your results with units in the table provided.
Series Combination
On the attached, sheet find the diagram of a series combination of three resistors with several labeled
points identified. A series combination like this can be included as part of a more complex circuit.
The equivalent resistance of a series combination is given by the formula𝑅𝑒𝑞 = 𝑅1 + 𝑅2 + 𝑅3 . If a
power supply is connected across the points F and E a the resulting circuit will have the following
properties.
2a)
b)
I.
The current will be the same throughout the circuit
II.
The sum of the voltages across the three resistors the same as the voltage across
points F and E.
Use the formula for equivalent resistance to calculate the equivalent resistance of your three
resistors. In doing the calculation use your measured values rather than the marked values.
Show your work
Now wire your three resistors into a series combination on your breadboard. Let your
instructor check the circuit if you have any doubts. Use the multimeter to measure the
equivalent resistance.
Now connect a power supply across points F and E and set it accurately to 5.00 V. Connect the
positive terminal of the power supply to point F. You may need to readjust the 5.00 V voltage to
that value from time to time.
3a)
Use your multimeter to measure the currents at points A, and B. Be careful to read the units
correctly and indicate the direction of the current at each of the point.
b)
What current would you expect to measure at points C and D. What directions do you
expect? Explain your reasoning. Use your multimeter to check. Let you instructor know if
your measurements differ from your expectations.
In a previous experiment you used a multimeter to measure the voltage difference across a resistor.
Here are some more details. Every point of a circuit has a voltage, and a voltmeter can be used to
measure the difference in voltage between any two points in a circuit. To be specific, when used as a
voltmeter, the number displayed on the multimeter is the voltage at the point connected to the 𝑉Ω
terminal minus the voltage at the point connected to the COM terminal. That number may be
positive or negative.
Voltage reading = 𝑉VΩ − 𝑉COM
4a)
b)
5.
Rotate your multimeter dial into the voltage range, and measure the voltage differences
indicated.
What voltages differences would you expect to measure across the points indicated? Explain
your reasoning in each case. Then make measurements and let you instructor know if your
measurements differ from your expectations.
You should expect that the equivalent resistance of your series combination will follow
Ohm’s law, 𝑉𝐹𝐸 = 𝐼𝑅𝑒𝑞 . Use your experimental values for those three quantities to check
that result.
Parallel Combinations
On the attached sheet find the diagram of three resistors in series with several points identified with
letters. A parallel combination like this can be included as part of a more complex circuit. When
resistors are configured in parallel they have an equivalent resistance given by
1
𝑅𝑒𝑞
1
1
1
=𝑅 +𝑅 +𝑅 .
1
2
3
If a power supply is connected across points G and H the resulting circuit will have the following
properties.
6a)
b)
I.
The sum of the currents through the resistors is the same as the current at points G or
H,
II.
The voltage across each of the resistors is the same as the voltage across points G and
H.
Use the formula to calculate the equivalent resistance of your three resistors in parallel. In
doing the calculation use your measured values rather than the marked values.
Now wire your three resistors into a parallel combination on your breadboard. Use the
multimeter to measure the equivalent resistance and compare with your calculated value.
Connect the power supply across points G and H and set it accurately to 5.00 V. Connect the
positive terminal of the power supply to point G. You may need to readjust the 5.00 V voltage to
that value from time to time.
7a)
Measure the voltage across the points indicated.
b)
Try to anticipate what voltage will be measured across the points indicated. Explain your
reasoning in each case. Then measure. Let your instructor know if your measurements differ
from your expectations.
8a)
Measure the currents at the points indicated and indicate the direction of the currents at those
points. Take care about units.
b)
What currents would you expect to be measured at the points indicated. Explain your
reasoning in each case. Then measure. Let your instructor know if your measurements differ
from your expectations.
You should expect the equivalent resistance of your parallel combination will follow Ohm’s
law, 𝑉𝐺𝐻 = 𝐼𝐺 𝑅𝑒𝑞 . Use your experimental values for those three quantities to check that
result.
9.
Mixed Series-Parallel Combinations
On the attached sheet, find the diagram of a mixed series-parallel combination. Combinations like
this can be included as part of a more complex circuit. The effective resistance of combinations like
this can be found by repeated application of the series and parallel formulas for equivalent
resistance. If a power supply is connected across points A and D the voltages and currents in the
various resistors can be found by application of the loop and junction rules.
10a)
b)
Use the series and parallel formulas to calculate the equivalent resistance of your three
resistors in this combination. In doing the calculation use your measured values of resistance
rather than the marked values.
Now wire your three resistors on your breadboard. Use the multimeter to measure the
equivalent resistance.
Connect the power supply across points A and D and set it accurately to 5.00 V. Connect the
positive terminal of the power supply to point A. You may need to readjust the 5.00 V voltage to
that value from time to time.
11a)
b)
Use your multimeter to measure the voltage differences indicated.
What voltage differences do you expect across the points indicated. Explain your reasoning
in each case. Then measure the voltages to check. Let your instructor know if your
measurements differ from your expectations.
12a)
b)
Use your multimeter to measure the currents at the points indicated.
What currents would you expect to be measured at the points indicated. Explain your
reasoning in each case. Then measure the currents to check. Let your instructor know if
your measurements differ from your expectations.
13.
Based on your data, what are the currents through the three resistors?
14.
You should expect the equivalent resistance of your mixed combination will follow Ohm’s
law, 𝑉𝐴𝐷 = 𝐼𝐷 𝑅𝑒𝑞 . Use your experimental values for those three quantities to check that
result.
Series and Parallel Combinations of Resistors
1.
Marked Resistance
Measured Values
𝑅1 = 220 Ω
𝑅2 = 330 Ω
𝑅3 = 470 Ω
Series Combination
2a)
Calculated equivalent resistance: ______________________
Show your work
b)
Measured equivalent resistance: _______________________
3a)
b)
𝐼𝐴 = _____________________
Direction (Circle one.)
toward B
away from B
𝐼𝐵 = _____________________
Direction (Circle one.)
toward C
away from C
𝐼𝐶 = _____________________
Explain your reasoning.
Direction (Circle one.)
toward D
away from D
𝐼𝐷 = _____________________
Explain your reasoning.
Direction (Circle one.)
toward E
away from E
Your expectations
4a)
𝑉𝐴 − 𝑉𝐵 = ______________________________
𝑉𝐵 − 𝑉𝐶 = ______________________________
𝑉𝐶 − 𝑉𝐷 = ______________________________
b)
𝑉𝐴 − 𝑉𝐷 = ______________________________
Explain your reasoning.
𝑉𝐴 − 𝑉𝐶 = ______________________________
Explain your reasoning.
𝑉𝐴 − 𝑉𝐹 = ______________________________
Explain your reasoning.
5.
Measured value of 𝑉𝐹𝐸
______________________________________
Measured I times measured 𝑅𝑒𝑞 __________________________
Parallel Combination
6a)
Calculated equivalent resistance: ______________________
Show your work.
b)
Measured equivalent resistance: _______________________
7a)
𝑉𝐴 − 𝑉𝐵 = ________________________________
𝑉𝐶 − 𝑉𝐷 = ________________________________
b)
𝑉𝐸 − 𝑉𝐹 = ________________________________ Explain your reasoning.
𝑉𝐸 − 𝑉𝐷 = ________________________________ Explain your reasoning.
𝑉𝐻 − 𝑉𝐶 = ________________________________ Explain your reasoning.
8a)
b)
9.
𝐼𝐴 = _____________________________________ Direction:
toward B
away from B
𝐼𝐶 = _____________________________________ Direction:
toward D
away from D
𝐼𝐸 = _____________________________________ Direction:
toward F
away from F
𝐼𝐺 = _____________________________________ Direction:
Explain
toward H
Measured value of 𝑉𝐺𝐻
______________________________________
Measured IG times measured 𝑅𝑒𝑞 __________________________
away from H
Mixed Series-Parallel Combination
10a)
Calculated equivalent resistance: ______________________
Show your work
b)
Measured equivalent resistance: _______________________
11a)
𝑉𝐴 − 𝑉𝐵 = _____________________________________
𝑉𝐵 − 𝑉𝐶 = _____________________________________
b)
𝑉𝐴 − 𝑉𝐶 = _____________________________________ Explain your reasoning
𝑉𝐸 − 𝑉𝐷 = _____________________________________ Explain your reasoning
12a)
𝐼𝐴 = ___________________________________________
𝐼𝐵 = ___________________________________________
𝐼𝐶 = ___________________________________________
b)
𝐼𝐸 = ___________________________________________ Explain your reasoning
𝐼𝐷 = ___________________________________________ Explain your reasoning
13.
𝐼𝑅1 = ___________________________________________
𝐼𝑅2 = ___________________________________________
𝐼𝑅3 = ___________________________________________
14.
Measured value of 𝑉𝐴𝐷
______________________________________
Measured IA times measured 𝑅𝑒𝑞 __________________________
Series Combination
Parallel Combination
Mixed Series-Parallel