Series and Parallel DC Circuits
In analyzing circuits, it is generally the current that is of interest. You have seen how Ohm’s Law can be
used to analyze very simple circuits consisting of an EMF and a single resistance. This method can be
extended to include circuits with more than one resistance, provided the resistances are in series or parallel
arrangements that can be replaced with an equivalent resistance.
Theory
When resistors are connected in series, there is a constant current through all of them (from the conservation
of charge). It can be shown that the group can be replaced with a single equivalent resistance given by
Req = R1 + R2 + R3 + . . .
(1)
Likewise, when resistors are connected in parallel, there will be the same potential drop across all of them.
It can therefore be shown that the group can be replaced with the equivalent resistance
1
1
1
1
=
+
+
+ ...
Req
R1
R2
R3
(2)
These equations can be applied multiple times when there are combinations of series and parallel arrangements of resistors within the same circuit.
Apparatus
Power supply, Pasco AC/DC Electronics Laboratory, Patch cords, DMM.
Procedure
Note: Do not leave the power supply on. Turn it on only when measuring potentials or
currents in a circuit - then turn it off.
1. Select three resistors - designated as R1 , R2 , and R3 - and determine their resistance (consult a color
code chart). Record these vales in Table 1.
2. Assemble the series combination of resistances as shown in Figure 1.
3. Using the values in Table 1, calculate the theoretical equivalent resistance for this circuit, using Equation 1. Record this in Table 2.
4. Measure the potential VT of and the current IT at the source. Using these values (with Ohm’s Law),
calculate the experimental equivalent resistance of the circuit. Compare the theoretical and experimental resistances.
1
5. Measure the potential drop across each individual resistor as well as the current through it.
6. Repeat the procedure with the parallel combination of resistances (Figure 2, Table 3).
7. Repeat the procedure with the series/parallel combination of resistances (Figure 3, Table 4).
Table 1: Resistors
R1 (Ω)
R2 (Ω)
R3 (Ω)
2
Figure 1: Series Resistances
Table 2: Analysis of Series Circuit
Theoretical equivalent resistance, Req (Ω)
Potential at source, VT (V)
Current at source, IT (A)
Experimental equivalent resistance (Ω)
Percent error in equivalent resistances
Potential drop across R1 , V1 (V)
Potential drop across R2 , V2 (V)
Potential drop across R3 , V3 (V)
Current through R1 , I1 (A)
Current through R2 , I2 (A)
Current through R3 , I3 (A)
3
Figure 2: Parallel Resistances
Table 3: Analysis of Parallel Circuit
Theoretical equivalent resistance (Ω)
Potential at source (V)
Current at source (A)
Experimental equivalent resistance (Ω)
Percent error in equivalent resistances
Potential drop across R1 (V)
Potential drop across R2 (V)
Potential drop across R3 (V)
Current through R1 (A)
Current through R2 (A)
Current through R3 (A)
4
Figure 3: Series/Parallel Combination of Resistances
Table 4: Analysis of Combination Circuit
Theoretical equivalent resistance (Ω)
Potential at source (V)
Current at source (A)
Experimental equivalent resistance (Ω)
Percent error in equivalent resistances
Potential drop across R1 (V)
Potential drop across R2 (V)
Potential drop across R3 (V)
Current through R1 (A)
Current through R2 (A)
Current through R3 (A)
5
Analysis
1. For your circuits, how close (in general) were the theoretical and experimental equivalent resistances?
Were Equations 1 and 2 verified in your opinion? What could account for the differences?
2. Comment (extensively) on potential in series and parallel circuits. Repeat for current.
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Pre-Lab: Series and Parallel DC Circuits
Section
Name
Answer the questions at the bottom of this sheet, below the line - continue on the back if you need more
room. Any calculations should be shown in full.
1. What is the common physical quantity in two resistors in series?
2. What is the common physical quantity in two resistors in parallel?
3. When two resistors are connected in series, how does the magnitude of the equivalent resistance compare
to the magnitudes of the individual resistances?
4. When two resistors are connected in parallel, how does the magnitude of the equivalent resistance
compare to the magnitudes of the individual resistances?
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