National University of Science & Technology (NUST)
School of Natural Science (SNS)
Department of Physics
APPLIED PHYSICS
 Abstract:
In this lab we used the apparatus given above to understand the variation in
current(I),voltage(V) and resistance(R) when resistances are connected in different
combinations. This lab consists of 4 different experiments in which the resistances
were connected in series, parallel and sometimes both. We shall note the different
readings of current(I),voltage(V) and resistance(R) by using a multimeter and
compare them with theoretical values. By the end we should be able to measure the
values of the 3 variables and understand there variation in different combinations.
 EXPERIMENT# 1 – OHM’s LAW:
Equipment Needed:
 AC/DC Electronics Lab Board: Wire Leads
 D-cell Battery
 Multimeter
 Graph Paper
Purpose
The purpose of this lab will be to investigate the three variables involved in a mathematical
relationship known as Ohm’s Law.
Theory
In electrodynamics we have studied the Ohm’s law. The ohm law gives us the relationship
between three important factors and electricity The factors being Resistance, current and
voltage. While studying the electrodynamics these factor are very important.
We performed the experiment on the lab board with different resistances to study the change
in current. And to verify the I/R ratio a graph is plotted.
Procedure
1. Choose one of the resistors that you have been given. Using the chart on the next page,
decode the resistance value and record that value in the first column of Table 3.1.
2. MEASURING CURRENT: Construct the circuit shown in Figure 3.1a by pressing
the leads of the resistor into two of the springs in the Experimental Section on the
Circuits Experiment Board.
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3.
Set the Multimeter to the 200 mA range, noting any special connections
needed for measuring current. Connect the circuit and read the current that is flowing
through the resistor. Record this value in the second column of Table 3.1.
4. Remove the resistor and choose another. Record its resistance value in Table 3.1 then
measure and record the current as in steps 2 and 3. Continue this process until you have
completed all of the resistors you have been given. As you have more than one resistor
with the same value, keep them in order as you will use them again in the next steps.
5. MEASURING VOLTAGE: Disconnect the Multimeter and connect a wire from the
positive lead (spring) of the battery directly to the first resistor you used as shown in
Figure 3.1b. Change the Multimeter to the 2 V DC scale and connect the leads as shown
also in Figure 3.1b. Measure the voltage across the resistor and record it in Table 3.1.
6. Remove the resistor and choose the next one you used. Record its voltage in Table 3.1
as in step 5. Continue this process until you have completed all of the resistors.
Reference
Data Processing
1. Construct a graph of Current (vertical axis) vs Resistance.
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Resistance Current Graph
16
14
12
Current
10
8
6
4
2
-50000
0
-2 0
50000
100000
150000
200000
Resistance
2. For each of your sets of data, calculate the ratio of Voltage/Resistance. Compare the
values you calculate with the measured values of the current.
Table 3.1
Trials
1
2
3
Experimental
Resistance (Ω)
197.3
99.1
3.3 k
Calculated
Current (mA)
5.63
11.20
0.336
Experimental
Voltage (V)
1.11
1.11
1.11
Coded
Resistance (Ω)
200
100
3.3 k
Experimental
current in (mA)
5.4
10.8
0.35
Questions:
1. From your graph, what is the mathematical relationship between Current and
Resistance?
Answer: The relationship between current and resistance is that they are inversely
proportional to each other.
Current
α 1 / Resistance
2. Ohm’s Law states that current is given by the ratio of voltage/resistance. Does your
data concur with this?
Answer: Yes According to the ohms law:
Current is equal to the ratio of voltage and resistance. When voltage is divided by the
resistance same result is obtained as measured by the ammeter.
3. What were possible sources of experimental error in this lab? Would you expect each
to make your results larger or to make them smaller?
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National University of Science & Technology (NUST)
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Answer: The possible error was due to the outdated apparatus and some
humanly errors occurred during the calculations.
To make the results clear, a mean can be calculated and then by calculating uncertainty.
The values would be made smaller to reduce error.
 EXPERIMENT# 2 – Resistances in Circuits:
Equipment Needed:
 AC/DC Electronics Lab Board: Wire Leads
 Multimeter
Purpose
The purpose of this lab is to begin experimenting with the variables that contribute to the
operation of an electrical circuit. This is the first of a three connected labs.
Theory
There are two main types of circuits parallel and series. The rules of finding the resistances,
the voltage and current are different in each case. So the experiment was performed in different
setups to study the changes in these variables. In series circuit the total resistance is the sum of
individual resistances and the current is same. While in parallel circuit the total resistance is
the sum of reciprocal of dividual resistances and the voltage is same.
Procedure
1. Choose three different resistors. Enter those sets of colors in Table 4.1 below. We will
refer to one as #1, another as #2 and the third as #3.
2. Determine the coded value of your resistors. Enter the value in the column labeled
“Coded Resistance” in Table 4.1. Enter the Tolerance value as indicated by the color of
the fourth band under “Tolerance.”
3. Use the Multimeter to measure the resistance of each of your three resistors. Enter these
values in Table 4.1.
4. Determine the percentage experimental error of each resistance value and enter it in the
appropriate column.
𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 𝐶𝑜𝑑𝑒𝑑
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝐸𝑟𝑟𝑜𝑟 =
× 100
𝐶𝑜𝑑𝑒𝑑
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National University of Science & Technology (NUST)
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Trials
1st
1
2
3
Red
Blue
Brown
Colors
2nd
3rd
Brown
Green
Black
Brown
Black
Orange
4th
Gold
Gold
Gold
Table 4.1
Coded
Resistance
210
65
10000
Measured
Resistance
% Error
Tolerance
0.268k
67.8
10.01k
27%
4.3%
0.09%
+5
+5
+5
5. Now connect the three resistors into the SERIES CIRCUIT, figure 4.1, using the spring
clips on the Circuits Experiment Board to hold the leads of the resistors together without
bending them. Measure the resistances of the combinations as indicated on the diagram
by connecting the leads of the Multimeter between the points at the ends of the arrows.
Series
R12 = 296.4 Ω
R23 = 3.39 k Ω
R123 = 3.59 k Ω
Figure 4.2
6. Construct a PARALLEL CIRCUIT, first using combinations of two of the resistors,
and then using all three. Measure and record your values for these circuits.
Parallel
NOTE: Include also 𝐑 𝟏𝟑 by
replacing 𝐑 𝟐 with 𝐑 𝟏 .
7.
Connect
the
COMBINATION
CIRCUIT
below
and
measure
the
various
combinations of resistance.
Do these follow the rules as
you
discovered
them
before?
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National University of Science & Technology (NUST)
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R12 = 65.97 Ω
R23 = 96.21 Ω
R123 = 64.67 Ω
Figure 4.2
Combination
R1 = 197.3 Ω
R23 = 96.21 Ω
R123 = 293.51 Ω
Figure 4.3
Questions:
1. How does the % error compare to the coded tolerance for your resistors?
Answer:
The %age error is much smaller as compared to the value of tolerance.
2. What is the apparent rule for combining equal resistances in series circuits? In parallel
circuits? Cite evidence from your data to support your conclusions.
Answer:
In the series circuit the total resistance is basically the product of resistance of value of
one resistor and total number of resistors attached. While in parallel Circuit the resistance of
one resistor is divided with total number of resistors attached to get the total resistance.
3. What is the apparent rule for combining unequal resistances in series circuits? In
parallel circuits? Cite evidence from your data to support your conclusions.
Answer:
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In the series circuit the sum of all the resistances of resistor is calculated
to get the total resistance. While in parallel to reciprocal of resistance is added to get
total resistance.
4. What is the apparent rule for the total resistance when resistors are added up in series?
In parallel? Cite evidence from your data to support your conclusions.
Answer:
When resistors are combined in series the total resistance is greater then the
individual resistances (For example R1 =197.3, R2=99.1, R3=3.3 k and R123=3.59 k)
but in parallel combination the total resistance is less than the individual resistances
(For example R1 =197.3, R2=99.1, R3=3.3 k and R123=64.67).
 EXPERIMENT# 3 – Voltages in Circuits:
Equipment Needed:
 AC/DC Electronics Lab Board: Wire Leads
 D-cell Battery
 Multimeter
Purpose
The purpose of this lab will be to continue experimenting with the variables that contribute to
the operation of an electrical circuit. You should have completed Experiment 4 before working
on this lab.
Theory
In this experiment, we take readings for resistance and voltage. For resistance, each resistor
will have a particular R value and since voltage splits up in a series circuit, voltage across each
resistor will add up for the total. Then, in a parallel circuit, voltage remains the same throughout
the circuit. Setting up the circuit in a combination of series and parallel, the voltage will divide
between R1 (that is in series) and R2 & R3 (together), but in between R2 & R3 that are
connected in parallel, voltage will remain the same across both resistors
Procedure
1. Connect the three resistors that you used in Experiment 4 into the series circuit shown
below, using the springs to hold the leads of the resistors together without bending
them. Connect two wires to the D-cell, carefully noting which wire is connected to the
negative and which is connected to the positive.
2. Now use the voltage function on the Multimeter to measure the voltages across the
individual resistors and then across the combinations of resistors. Be careful to observe
the polarity of the leads (red is +, black is -). Record your readings below.
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National University of Science & Technology (NUST)
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Series:
R1 = _ 100.4 k Ω
R2 =__99.1 Ω
V1 = 1.14 𝑉
V2 = 0.0011 𝑉
R3 = __3.3 k Ω
V3 = 0.0368 𝑉
R12 = _ 100.5_k Ω
V12 = 1.411 𝑉
R23 =
3.4 k Ω
R123= 103.8 k Ω
V23 = 0.0379 𝑉
V123= 1.1779 𝑉
3. Now connect the parallel circuit below, using all three resistors. Measure the voltage
across each of the resistors and the combination, taking care with the polarity as before.
NOTE: Keep all three resistors connected throughout the time you are making your
measurements. Write down your values as indicated below.
Parallel
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R1 =
100.4 k Ω
V1 = 1.12 𝐕
R2 =
99.1 Ω
V2 = 1.12 𝐕
R3 =
3.3 k Ω
V3 = 1.12 𝐕
Ω
V123 = 1.12 𝐕
R123 =
96.12
Figure 5.2
4. Now connect the circuit below and measure the voltages. You can use the resistance
readings you took in Experiment 4 for this step.
Combination
R1 = 100.4 k Ω
V1 = 1.14 𝐕
R23 = 96.21 Ω
V23 = 0.038 𝐕
R123 = 100.5 k Ω
V123 =1.178 𝐕
Figure 5.3
Questions:
1. On the basis of the data you recorded on the table with Figure 5.1, what is the pattern
for how voltage gets distributed in a series circuit with equal resistances?
Answer: According to the data, if we connect multiple resistances in series the voltage
gets divided across all the resistances.
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National University of Science & Technology (NUST)
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2. Utilizing the data from Figure 5.2, what is the pattern for how voltage distributes itself
in a parallel circuit for unequal resistances?
Answer: However, in parallel circuit the voltage remains the same no matter how many
resistances we connect in parallel combination.
3. Do the voltages in your combination circuits (see Figures 5.3) follow the same rules as
they did in your circuits which were purely series or parallel? If not, state the rules you
see in operation.
Answer: Yes, it follows the same rule in the circuit shown in the figure. Across R1 and
the junction for R2 and R3 the voltage gets divided. While in the parallel circuit between
R2 and R3 the voltage remains the same.

EXPERIMENT# 4 – Current in Circuits:
Equipment Needed:
 AC/DC Electronics Lab Board: Wire Leads
 D-cell Battery
 Multimeter
Purpose
The purpose of this lab will be to continue experimenting with the variables that contribute to
the operation of electrical circuits.
Theory
Here we simply measure the current in a series and parallel circuit, as well as voltage and
resistance. Current stays same throughout a series circuit, but it splits up in a parallel circuit.
As seen in Experiment 5, voltage split up in a series circuit but remains the same in a parallel
circuit. Resistance in series circuit is found by adding each resistance while in parallel circuit,
it is found by using the formula 1/Rt = 1/R1 + I/R2 + I/R3 + ..
Procedure
1. Connect the same three resistors that you used in Experiments 3 and 4 into the series
circuit shown below, using the springs to hold the leads of the resistors together without
bending them. Connect two wires to the D-cell, and carefully note which lead is
negative and which is positive.
Series
2. Now change the leads in your DMM so that they can be used to measure current. You
should be using the scale which goes to a maximum of 200 mA. Be careful to observe
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the polarity of the leads (red is +, black is -). In order to measure current, the
circuit must be interrupted, and the current allowed to flow through the meter.
Disconnect the lead wire from the positive terminal of the battery and connect it to the
red (+) lead of the meter. Connect the black (-) lead to R1, where the wire originally
was connected. Record your reading in the table as Io. See Figure 6.3.
3. Now move the DMM to the positions indicated in Figure 6.3, each time interrupting the
circuit, and carefully measuring the current in each one. Complete the table on the top
of the back page.
NOTE: You will be carrying values from Experiments 3 and 4 into the table on the back.
R1 =100.4 k Ω
I0 =11.2 µ𝐴
V1 =1.124 𝑉
R2 =99.1 Ω
I1 =11.2 µ𝐴
V2 =1.1 m𝑉
R3 =3.3 k Ω
I2 =11.2 µ𝐴
V3 =0.036 𝑉
R12 = 100.5 k Ω
I3 =11.2 µ𝐴
V12 =1.126 𝑉
R23 =3.4 kΩ
V23 =0.038 𝑉
R123=103.8 k Ω
V123=1.163 𝑉
Parallel
4. Connect the parallel circuit below, using all three resistors. Review the instructions for
connecting the DMM as an ammeter in step 2. Connect it first between the positive
terminal of the battery and the parallel circuit junction to measure I0. Then interrupt the
various branches of the parallel circuit and measure the individual branch currents.
Record your measurements in the table below.
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National University of Science & Technology (NUST)
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R1 = 100.4 kΩ
I1 =0.011 𝒎𝑨
R2 = 99.1 Ω
I2 =0.011 𝑨
V2 = 1.12𝐕
R3 = 3.3 kΩ
I3 =0.34 𝒎𝑨
V3 = 1.12𝐕
R123 = 96.12 Ω
I0 =0.012 𝑨
V1 = 1.12𝐕
V123 = 1.12𝐕
I4 = 0.012 𝑨
Questions:
1. On the basis of your first set of data, what is the pattern for how current behaves in a
series circuit? At this point you should be able to summarize the behavior of all three
quantities - resistance, voltage and current - in series circuits.
Answer: In a series circuit, current stays the same at all points in the circuit while
voltage splits up based on the magnitude of the resistance of each resistor. The total
resistance is addition of all the individual resistances.
2. On the basis of your second set of data, are there any patterns to the way that currents
behave in a parallel circuit? At this time you should be able to write the general
characteristics of currents, voltages and resistances in parallel circuits.
Answer: In a parallel circuit, current splits up based on the magnitude of the resistance
of each resistor. Voltage remains the same at every point in the circuit and the addition
of the inverse of each resistance gives the total resistance of the circuit.
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
Results and conclusions:
After performing all the experiments, we practically and experimentally verified
the OHM’s law. That V = I*R . Current is inversely proportional to resistance and
directly proportional to voltage. We plotted graph and also put values experimentally
to prove OHM’s law.
 Discussion:
The equivalent values of current(I),voltage(V) and resistance(R)
vary differently in parallel and series combinations and follow OHM’s law which states
V=IR. We were to find these values using a multimeter and sometimes compare them
with theoretical values. If these values follow OHM’s law then the measurements are
correct. If not then there is some error in our measurements which might have been
caused by faulty apparatus or mistakes made by us during measurement. From these
experiments we found that the value of voltage of the battery is divided among the
resistances. If the resistances are equal then the voltage is equally divided. In case of
different resistances the value of potential difference is different across all resistances.
While the current is same throughout the circuit and the equivalent resistance is sum of
all the resistances. In case of parallel circuit, the current is distributed for all resistances
while the voltage supplied to each resistance is the same. Similarly the reciprocal of
equivalent resistance is equal to the sum of reciprocal of all resistances.
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