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Series Circuits
Problem:
What are the mathematical relationships between current, voltage, and resistance in
series circuits?
Materials:
Ammeter, voltmeter, power source, connecting wires, and various resistors, switch.
Procedure:
1. Connect a resistor, R1, to a
voltage source and measure the
current through the resistor and the
voltage across it as shown in figure 1.
V
A1
R
R1
V1
Figure 1
Current A1 = _____ Voltage V1 = _____ Calculated resistance R1 = _____
How does your calculated value compare to the manufacturers rated values?
2. Modify the circuit to include two
resistors in series as shown in Figure 2.
Keep the same total voltage (V). Before
you close the switch, make a few
predictions.
A3
A1
V2
V1
A2
R1
R2
V3
Figure 2
How do you think V1 in Part 2 will compare to V1 in Part 1?
It will be ___ greater ___ less ___ the same. (check one).
How do you think A1 in Part 2 will compare with A1 in Part 1?
It will be ___ greater ___ less ___ the same. (check one).
Again measure the appropriate currents and voltages.
Current A1 = ________ Voltage V1 = ________ Calculated resistance R 1 = ________
Current A2 = ________ Voltage V2 = ________ Calculated resistance R 2 = ________
Current A3 = ________ Voltage V3 = ________ Calculated resistance R Total = _____
Sum of resistance R1 + R2 = _________
Adapted with permission from the Comprehensive Conceptual Curriculum for Physics (C3P), Richard P. Olenick, University of
Dallas, Irving, TX (2000). Copyright 2000 by Richard P. Olenick, University of Dallas.
3. Modify the circuit to include three resistors in series as shown in Figure 3. Keep
the same voltage (V). Before you close the switch, make a few predictions.
A3
A1
V1
V2
V3
R2
R3
A2
R1
V4
Figure 3
How do you think V1 in Part 3 will compare to V1 in Part 2?
It will be ___ greater ___ less ___ the same. (check one).
How do you think A1 in Part 3 will compare with A1 in Part 2?
It will be ___ greater ___ less ___ the same. (check one).
Again measure the appropriate currents and voltages.
Current A1 = ________ Voltage V1 = ________ Calculated resistance R 1 = ________
Current A2 = ________ Voltage V2 = _________ Calculated resistance R 2 = _______
Current A3 = ________ Voltage V3 = ________ Calculated resistance R 3 = ________
Voltage V4 = _________ Calculated resistance R total = _________
Sum of resistance R1 + R2 + R3 = _________
Summing Up:
1. Write a summary relationship describing the relationship between;
a. the currents
b. the potential differences (voltages)
c. the resistances
2. How did the value of your predicted currents in A1 and A3 compare with the
observed values?
3. Give a reasonable explanation for any variation in your predicted value and the
observed value. (Experimental error, miscalculation and human error won’t be
accepted.)
Adapted with permission from the Comprehensive Conceptual Curriculum for Physics (C3P), Richard P. Olenick, University of
Dallas, Irving, TX (2000). Copyright 2000 by Richard P. Olenick, University of Dallas.
Series Circuits
Teacher’s Notes
Teaching Strategies:
The resistance of the resistors could be made to be equal if you think the students
might have difficulty with seeing the application of Ohm's Law to series circuits. It is
felt that in Part 3 the students should be able to generalize their results from Part 2.
Concepts associated with electricity often require formal reasoning. Observations can
be made more concrete by using flashlight bulbs instead of resistors. The resistances
will not be known, but they will be the same and the brightness of the bulbs will
decrease with then decreasing currents in part 2 and 3.
In comparing calculated values of resistance from measured values of current and
voltage with manufacturer's resistance values it should be recognized that the meters
have the effect of serving as a resistor. The ammeter is a low resistance instrument
but if the resistors are small, then there could be an effective potential drop across the
ammeter. The voltmeter is a high resistance instrument. Always place it in parallel in
the circuit with the resistor of the circuit. If the resistor of the circuit is low compared
to the resistance of the voltmeter, then the voltmeter will draw little current. However,
if the value of the resistor in the circuit is very large, then there could be a significant
current through the meter.
Note: Many schools today use multimeters. These work well. The students should be
shown how to move one multimeter around to measure all the value requested.
The students should be able to apply Ohm's Law in order to calculate the value of
each resistor. Another value for this activity is for the students to be able to translate a
circuit diagram into an actual wiring pattern. You may wish to have your students
check their wiring patterns before turning the switch "on". They should close the
switch very briefly the first time to make sure the ammeter isn’t driven off scale
Sample Calculations/Expected Results:
1. R(actual) = 4 ohms
I = 1.45 amps
V = 6 volts
R(cal) = V = 6 volts
= 4.1 ohms
I 1.45 amps
2. R1 = R2 = 4 ohms
I1 = .7 amp, I2 = .7 amp
V1 = 3 volts, V2 = 3 volts
R1(cal) = V1 = 3 volts = 4.3 ohms
I1
.7 amps
R2(cal) = V2 = 3 volts =
I2 .7 amps
4.3 ohms
Adapted with permission from the Comprehensive Conceptual Curriculum for Physics (C3P), Richard P. Olenick, University of
Dallas, Irving, TX (2000). Copyright 2000 by Richard P. Olenick, University of Dallas.
3. R1 = R2 = R3 = 4 ohms
I1 = .4 amp, I2 = .4 amp, I3 = .7 amp
V1 = 2 volts, V2 = 2 volts, V3 = 3 volts and V4 = 6 volts
R1(cal) = V1 = 2 volts = 5 ohms
I1
.4 amps
R2(cal) = V2 = 2 volts =
I2 .4 amps
5 ohms
R3(cal) = V1 = 2 volts = 5 ohms
I1
.4 amps
Rtotal(cal) = V2 = 6 volts =
I2
.4 amps
15 ohms
Summing Up:
1. Within expected variations due to the accuracy of the readings and the effects of
the instruments on the circuits the following relationships should be
demonstrated:
a. Currents in a series circuit are everywhere the same.
b. Potential differences (voltages) across the resistors add up to equal the total
potential difference across the circuit or the power supply.
c. The total resistance of a circuit is equal to the sum of the individual resistors.
2. The measured currents are probably a little lower than those predicted by Ohm’s
Law.
3. Because of meter resistance, the process of measuring the value alters the value.
Also, when the circuit is left on the resistors get hot, altering the resistance and
the current.
Adapted with permission from the Comprehensive Conceptual Curriculum for Physics (C3P), Richard P. Olenick, University of
Dallas, Irving, TX (2000). Copyright 2000 by Richard P. Olenick, University of Dallas.