EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
EXPERIMENT 1
SERIES-PARALLEL RESISTANCE
OBJECTIVES
1.
2.
3.
4.
Test the theoretical analysis of series-parallel circuit through direct measurements.
Improve skills of identifying series and parallel elements.
Measure properly the resistance, voltages and currents of a series-parallel circuit.
Practice applying Kirchhoff’s laws, the voltage divider and current divider rules.
INTRODUCTION
SERIES-PARALLEL RESISTANCE
The most common connections found in circuit analysis are series or parallel connections. Several
resistors can be combined to represent a single equivalent resistance for the purpose of circuit
simplifying. The equivalent resistance for any number of resistors in series connection is the sum of
each individual resistor or simply by adding all single resistors. The single equivalent resistor is
always larger than the largest resistor in the series connection. Resistors connected in series carry
the same current thru them but the voltage across each of the resistors can be obtained using
voltage divider rule principle or Ohm’s law.
N
Req ( SERIES )  R1  R2  R3  R4  R5    RN   Rn
(1.1)
n 1
Meanwhile the equivalent resistance for any number of resistors in parallel connection is obtained
by taking the reciprocal of the sum of the reciprocal of each single resistor in the circuit. The single
equivalent resistor is always smaller than the smallest resistor in the parallel connection. The voltage
across each resistor must be the same but the currents thru each of them are divided according to
the current divider rule principle.
1

1
1
1
1
Req ( PARALLEL)   



   R N 
 R1 R2 R3 R4 R5

1
N 1
 
 n 1 Rn



1
(1.2)
KIRCHHOFF’S LAWS
Kirchhoff’s Current Law (KCL) states that the algebraic sum of current entering a node must be equal
to that of leaving the same node.
Applying KCL, we obtain
i3
i4
i2
i2 + i6 = i1 + i3 + i4 + i5
i1
i5
i6
For this particular problem, given
one unknown but all others are
known, we can solve using the
above single equation.
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Lab 1: Series-Parallel Resistance
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
Mathematically we write,
N
M
 in ( Into) 
i
n 1
m 1
m
(1.3)
(Out )
where N = no of current entering the node and M = no of current leaving the node.
Y
or
i
y 1
y
0
Y = no of total current at the node
(1.4)
Kirchhoff’s Voltage Law states that the algebraic sum of voltage drop in a loop must be equal to that
of voltage rise in the same loop. Stated it in a different way is that the algebraic sum of all voltages
around a loop must be zero.
Applying KVL, we obtain
+ V1 + V4 -
Loop 1
R2
R4
Is
Loop 2
R3
+ VIs -
Vs
+ V2 -
R1
- V3 +
Loop 1: V1 + V2 + V3 = Vs
Loop 2: V4 + VIs = V2
Remember that the number of
unknowns to be solved must
equal to the number of equations
generated.
Mathematically we write,
N
V
n 1
n
( Drop ) 
M
V
m 1
m
( Rise )
where N = no of voltage drop in the loop and M = no of voltage rise in the loop.
Y
or
V
y 1
y
0
Y = no of total voltage in the loop
(1.5)
You can try to prove that using KVL elements in parallel connection should have same voltage across
them. While using KCL try to prove that elements in series should carry same current through them.
EQUIPMENT/COMPONENT
Multimeter (1)
Variable DC Power Supply (1)
Resistor (1/4 W) – 2.2 k, 1 k , 3.9 k, 4.7 k, 6.8 k
Breadboard (1)
**For all theoretical calculation results students are strictly required to show their work in progress
(formula form/complete figures) in the PRE-LAB space provided before the lab session. Otherwise
they will be forbidden from participating the session. There will be certain marks allocated for this
part.
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Lab 1: Series-Parallel Resistance
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
PROCEDURE
1. Construct the circuit as shown in Figure 1 using the breadboard and insert the measured value
of each resistor in Table 1. Using multimeter, measure actual resistances between terminals B-C,
A-C, B-D and A-D. Calculate the percentage difference between the calculated and measured
values. Record all your answers in Table 2.
R2 = 6k8 
B
A
R1 = 1k0 
I2
R3 = 3k9 
C
D
R5 = 2k2 
I3
R4 = 4k7 
I4
Figure 1: Circuit diagram of a series-parallel resistance connection
2. Construct the circuit as shown in Figure 2 using the breadboard. Supply a fixed 5V source from
the DC power supply once the circuit is constructed and carefully checked. Using voltmeters
placed in parallel with the elements whose voltage are to be measured, obtain V1, V2 and V3.
Calculate the percentage difference between the calculated and measured values. Record all
your answers in Table 3.
V2
R2 = 6k8 
V1
B
A
R1 = 1k0 
I2
R3 = 3k9 
I3
R4 = 4k7 
V3
C
D
R5 = 2k2 
I4
A1
Vs = 5 V
IT
Figure 2: Connecting voltage source and multimeters to a series-parallel circuit
3. Insert ammeters in series with the elements whose currents are to be measured such as in
Figure 2. Obtain I2, I3 and I4. Calculate the percentage difference between the calculated and
measured values. Record all your answers in Table 3.
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Lab 1: Series-Parallel Resistance
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
RESULT
Resistor (Nominal
Value ± tolerance)
3k3  ± 5%
1k0 
6k8 
3k9 
4k7 
2k2 
Color Bands – Color
2nd
3rd
1st
Orange
orange
4th
red
gold
Measured
Resistance
nil
Table 1: Reading resistance values by color-coding and actual measurement
Resistance
Terminal
Calculated (k)
Measured (k)
% Difference
B-C
A-C
B-D
A-D
Table 2: Series-parallel equivalent resistances
Circuit Variables
Calculated (k)
Measured (k)
% Difference
V1
V2
V3
I2
I3
I4
Table 3: Determining circuit variables using basic analysis methods
*Mark for calculation given in PRE-LAB section
For the percentage difference calculation you can use the following equation:
% Difference 
Calculated  Measured
X 100%
Calculated
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Lab 1: Series-Parallel Resistance
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
PRE-LAB CALCULATION (Show your WIP)
(All calculations should be done in rms values)
1. Identify the nominal value together with its tolerance of each resistor using color coded method
you learnt in the previous lab activity. Record in the space provided in Table 1 as shown by the
example.
2. Referring to Figure 1 show the calculation of equivalent resistance for each pair of terminals, BC, A-C, B-D and A-D using the designations given. Place the numerical answers in TABLE 2 (after
plugging in the actual measured resistance values).
3. Calculate the total resistance, RT and then total current, IT of the circuit in Figure 2. Simplify the
circuit into a single loop. Draw the equivalent circuit including the details. From the simplified
circuit, using KVL calculate V1, V2 and V3. Show all your calculation work and insert the final
answers into TABLE 3 (after re-calculate the answers using the measured resistance values).
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Lab 1: Series-Parallel Resistance
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
4. Using current divider rule (derived from KCL) calculate I2, I3 and I4 in the circuit of Figure 2. Show
all your calculation work together with all simplified circuit stages in and insert the final answer
into TABLE 3 (after re-calculate the answers using the measured resistance values).
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Lab 1: Series-Parallel Resistance
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
EVALUATION QUESTIONS
1. From the percentage difference in Table 2 and Table 3, how do the measured values compared
to the calculated values? What do you think are the factors that contribute to the differences?
Give at least two factors (2).
Answer:
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2. State two (2) considerations in determining the equivalent resistance of resistive circuits?
Answer:
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3. Verify the Kirchhoff’s voltage law from your practical results in the step 2 of the procedure.
Answer:
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4. Verify the Kirchhoff’s current law from your practical results in the step 7 of the procedure at
point C.
Answer:
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5. What relationship did RAB have on the smallest parallel resistor in this experiment?
Answer:
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Lab 1: Series-Parallel Resistance
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
6. If the lights on your Christmas tree are wired in series, what will happen when one bulb burns
out? What will happen if the bulbs are wired in parallel?
Answer:
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7. When can we use voltage divider rule and current divider rule?
Answer:
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8. Try to analyze the circuit in Figure E1 and solve for VJ. Determine IJ if given I1=0.47A and I2=0.12
A. Show all your calculation works.
Figure E1: Circuit for problem 8
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Lab 1: Series-Parallel Resistance