Universiti Malaysia Perlis
DKT 111/3 – ELECTRIC CIRCUITS PRINCIPLES
LAB ASSIGNMENT 2
SERIES-PARALLEL RESISTANCE
Pn. Nazatul Syima Bt. Saad
Pusat Pengajian Kejuruteraan Komputer Dan Perhubungan
Universiti Malaysia Perlis
DKT111/4 ELECTRIC CIRCUIT PRINCIPLE
LABORATORY MODULE
EXPERIMENT 2
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.
Mathematically we write,
2
Universiti Malaysia Perlis (UniMAP)
Lab 2: Series-Parallel Resistance
DKT111/4 ELECTRIC CIRCUIT PRINCIPLE
N
i
n 1
n
LABORATORY MODULE
( Into) 
M
i
m 1
m
(Out )
(1.3)
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.
+ V1 + V4 Applying KVL, we obtain
Loop 1
R2
R4
Loop 2
R3
Is
+ VIs -
Vs
+ V2 -
R1
Remember that the number of
unknowns to be solved must
equal to the number of equations
generated.
- V3 +
Mathematically we write,
N
V
n 1
n
Loop 1: V1 + V2 + V3 = Vs
Loop 2: V4 + VIs = V2
( 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.
3
Universiti Malaysia Perlis (UniMAP)
Lab 2: Series-Parallel Resistance
DKT111/4 ELECTRIC CIRCUIT PRINCIPLE
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.
4
Universiti Malaysia Perlis (UniMAP)
Lab 2: Series-Parallel Resistance
DKT111/4 ELECTRIC CIRCUIT PRINCIPLE
LABORATORY MODULE
RESULT
Resistor (Nominal
Value ± tolerance)
3k3  ± 5%
1k0 
6k8 
3k9 
4k7 
2k2 
1st
Orange
Color Bands – Color
2nd
3rd
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
calculation
given in difference
PRE-LAB section
Forfor
the
percentage
calculation
% Difference 
you can use the following equation:
Calculated  Measured
X 100%
Calculated
5
Universiti Malaysia Perlis (UniMAP)
Lab 2: Series-Parallel Resistance
DKT111/4 ELECTRIC CIRCUIT PRINCIPLE
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, B-C, 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).
6
Universiti Malaysia Perlis (UniMAP)
Lab 2: Series-Parallel Resistance
DKT111/4 ELECTRIC CIRCUIT PRINCIPLE
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).
7
Universiti Malaysia Perlis (UniMAP)
Lab 2: Series-Parallel Resistance
DKT111/4 ELECTRIC CIRCUIT PRINCIPLE
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:
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
2. State two (2) considerations in determining the equivalent resistance of resistive circuits?
Answer:
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
3. Verify the Kirchhoff’s voltage law from your practical results in the step 2 of the
procedure.
Answer:
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
________________
4. Verify the Kirchhoff’s current law from your practical results in the step 7 of the
procedure at point C.
Answer:
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
8
Universiti Malaysia Perlis (UniMAP)
Lab 2: Series-Parallel Resistance
DKT111/4 ELECTRIC CIRCUIT PRINCIPLE
LABORATORY MODULE
5. What relationship did RAB have on the smallest parallel resistor in this experiment?
Answer:
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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:
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
7. When can we use voltage divider rule and current divider rule?
Answer:
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
DISCUSSION:
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
~ooooOOOOOoooo~
9
Universiti Malaysia Perlis (UniMAP)
Lab 2: Series-Parallel Resistance