Lab Name: (a) To perform DC analysis of Ohms Law (b) To perform DC analysis of Kirchhoff’s Laws
(KCL and KVL).
Course title: Industrial Electronics
Total Marks: ___20_________
Practical No. 2
Date of experiment performed: ____________
Course teacher/Lab Instructor: Engr. Muhammad Usman
Date of marking: ____________
Student Name:__________________________
Registration no.__________________________
Marking Evaluation Sheet
Knowledge components
Domain
Taxonomy level
Contribution
Max.
marks
1. Student is aware with requirement
and use of apparatus involved in
experiment.
2. Student has conducted the
Psychomotor
experiment by practicing the
hands-on skills as per instructions.
3. Student has achieved required
accuracy in performance.
Manipulate (P2)
Precision (P3)
-
4. Student aware of discipline &
safety rules and followed the rules
during experiment.
Receiving (A1)
2
5. Student has responded well and
contributed affectively in
respective lab activity.
6. Student has applied theoretical
knowledge to obtain and report
the results.
Affective
Obtained
marks
3
Imitation (P1)
70%
11
20%
2
Respond (A2)
Apply
Cognitive
10%
2
Total
20
Normalize
marks out of
(5)
5
(C3)
Signed by Course teacher/ Lab Instructor
EXPERIMENT No. 02
(a) To perform DC analysis of Ohms Law
(b) To perform DC analysis of Kirchhoff’s Laws (KCL and KVL).
PRE LAB TASK
Objectives
1. To understand the relationship between current & voltage for a resistor.
2. To verify the characteristics of series & parallel resistive network.
3. To learn how to write KVL equation for any closed loop.
4. To learn how to apply KCL at any node in electrical circuits.
5. To learn how to calculate electrical parameters in a circuit using KVL and KCL.
Introduction
A resistive circuit is a circuit containing only resistors and ideal current and voltage sources.
Analysis of resistive circuits is less complicated than analysis of RLC circuits containing
capacitors and inductors. If the sources are constant (DC) sources, the result is a DC circuit.
Any circuit that is built using Resistors only as basic building block, except for connecting wires
and power supply, is generally called Resistive Network.
Whenever a resistor is connected to battery, current starts flowing through it and a voltage develops
across that resistor, depending upon the resistance it is offering.
Theory
Series Circuit
When all the resistive components of a circuit are connected end to end to form a single path for
flow of current, then the circuit is referred as series circuit. The manner of connecting components
end to end is known as series connection.
Suppose we have n number of resistors R1, R2, R3............Rn and they are connected in end to end
manner, means they are series connected. If this series combination is connected across a voltage
source, the current starts flowing through that single path. As the resistors are connected in end
to end manner, the current first enters into R1, then this same current comes in R2, then R3 and at
last it reaches Rn from where the current enters into the negative terminals of the voltage source .
In this way, the same current circulates through every resistor connected in series. Hence, it can
be concluded that in a series circuit, the same current flows through all parts of the electrical
circuit.
Again according to Ohm’s law , the voltage drop across a resistor is the product of its electrical
resistance and the current flow through it. Here, current through every resistor is the same, hence
the voltage drop across each resistor's proportional to its electrical resistance value. If the
resistances of the resistors are not equal then the voltage drop across them would also not be equal.
Thus, every resistor has its individual voltage drop in a series circuit. The total resistance offered
by the series circuit is equal to the sum of all resistance connected in the circuit and also the sum
of the voltage drops is equal to the voltage applied across the three conductors.
Parallel Circuit
When two or more electrical components are connected in a way that one end of each component
is connected to a common point and the other end is connected to another common point, then the
electrical components are said to be connected in parallel, and such an electrical circuit is referred
as a parallel circuit. In this circuit every component will have the same voltage drop across them,
and it will be exactly equal to the voltage which occurs between the two common points where the
components are connected. Also in a parallel circuit, the current has several parallel paths
through these parallel connected components, so the circuit current will be divided into as many
paths as the number of components.
Here in this electrical circuit, the voltage drop across each component is equal. Again as per Ohm’s
law, voltage drop across any resistive component is equal to the product of its electrical resistance
and current through it. As the voltage drop across every component connected in parallel is the
same, the current through them is inversely proportional to its resistance value.
Ohms Law:
Ohm’s law states that the voltage drop across a resistor is the product of its electrical resistance
and the current flow through it.
Kirchhoff’s Voltage Law (KVL)
Kirchhoff’s Voltage Law or KVL, states that “in any closed loop network, the total voltage around
the loop is equal to the sum of all the voltage drops within the same loop”. In other words, the
algebraic sum of all voltages drops within the loop must be equal to zero. This idea by Kirchhoff
is known as the Conservation of Energy.
Mathematically,
𝑛
∑ 𝑉𝑘 = 0 … … … … (1)
𝑘=1
th
Here, n is the total number of voltages and Vkis the K voltage.
The algebraic sum is the sum which takes into account the polarities of the voltage drops. The sign
of the voltage drop across a resistor depends on the direction of current through that resistor but is
independent of the polarity of any other source of e.m.f. in the circuit under consideration. To
determine this law, we need to know the algebraic sign.
➢ When current flows from lower potential to higher potential it is considered positive.
➢ When current flows from higher potential to lower potential it is considered negative.
Figure 1
Applying Kirchhoff’s voltage law to the first and the second loops in the circuit shown in Figure
1 yields:
Loop abdea:
𝑉𝑆 − 𝑉𝑅1 − 𝑉𝑅2 − 𝑉𝑅5 = 0 … … … … … (2𝑎)
Loop bcdb:
−𝑉𝑅3 − 𝑉𝑅4 − 𝑉𝑅2 = 0 … … … … … (2𝑏)
Kirchhoff’s Current Law (KCL)
Kirchhoff’s Current Law or KCL, states that the “total current or charge entering a junction or
node is exactly equal to the charge leaving the node as it has no other place to go except to leave,
as no charge is lost within the node”. In other words, the algebraic sum of all the currents entering
and leaving a node must be equal to zero, I(exiting) + I(entering) = 0. This idea by Kirchhoff is
commonly known as the Conservation of Charge.
Mathematically:
𝑛
∑ 𝐼𝑘 = 0 … … … … (3)
𝑘=1
Here, n is the total number of currents flowing towards or away from the point and Ik is the
th
K current.
Applying Kirchhoff’s current law to the first four nodes in the circuit shown in Figure1 yields the
following equations:
Node a:
𝐼𝑆 − 𝐼1 = 0 … … … … … (3𝑎)
Node b:
𝐼1 − 𝐼2 − 𝐼3 = 0 … … … … … (3𝑏)
Node c:
𝐼3 − 𝐼4 = 0 … … … … … (3𝑐)
Node d:
𝐼2 − 𝐼4 − 𝐼5 = 0 … … … … … (3𝑑)
Voltage Divider Rule:
The voltage divider rule is used to solve circuits to simplify the solution. Applying this rule
can also solve simple circuits thoroughly The main concept of this voltage divider rule is “
The voltage is divided between two resistors which are connected in series in direct proportion
to their resistance. Voltage divider involves of two important parts they are the circuit and the
equation.
Current Divider Rule:
The main concept of this rule is “The electrical current entering the node of a parallel circuit
is divided into the branches. Current divider formula is employed to calculate the magnitude
of divided current in the circuits.”
Laws of equivalent Resistance:
The total resistance of the circuit is found by simply adding up the resistance values of the
individual resistors: Equivalent resistance of resistors in series: R = R1 + R2 + R3 + ….
The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the
resistance values, and then taking the reciprocal of the total: Equivalent resistance of resistors
in parallel: 1 / R = 1 / R1 + 1 / R2 + 1 / R3 +...
Summary of Laws:
If we wish to calculate the current passing through and voltage across each resistor in a circuit
we use laws as:
1. Ohms law:
Ohm's law states that the current through a conductor between two points is directly
proportional to the voltage across the two points.
Mathematically:
2. Kirchhoff’s Voltage Rule:
This law is also called Kirchhoff's second law, Kirchhoff’s loop (or mesh) rule, and
Kirchhoff's second rule. This law states that:
“The directed sum of the potential differences (voltages) around any
closed loop is zero.”
Mathematically:
3. Kirchhoff’s Current Rule:
This law is also called Kirchhoff's first law, Kirchhoff's point rule, or
Kirchhoff's junction rule (or nodal rule). This law states that:
“For any node (junction) in an electrical circuit, the sum of currents
flowing into that node is equal to the sum of currents flowing out of that
node” or equivalently:
“The algebraic sum of currents in a network of conductors meeting at a
point is zero.”
Mathematically:
4. Current Divider Rule:
5. Voltage Divider Rule:
6. Law of Equivalent Resistance:
The total resistance of the circuit is found by simply adding up the resistance values of the
individual resistors: Equivalent resistance of resistors in series: R = R1 + R2 + R3 + ….
The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the
resistance values, and then taking the reciprocal of the total: Equivalent resistance of resistors
in parallel: 1 / R = 1 / R1 + 1 / R2 + 1 / R3 +...
All of the above-mentioned techniques are used for numerical evaluations of circuit. For
practical evaluation of any network/circuit, Digital Multimeter is the best solution as well as
option.
Circuit Diagram
Fig.1I. Circuit for Analysis.
Useful Formulas:
Using Equivalent/Total resistance calculation formula, we can write:
R eq =
R2 ×R3
R2 +R3
(1)
And
R T = R eq + R1
So we can write now, using Ohms Law:
(2)
I1 =
V1
RT
(3)
This is the current passing through resistor R1. Now I2 and I3 can be calculated by using current
division rule as:
R3
) × I1
I2 = (
R2 + R3
(4)
And
I3 = (R
R2
2
+R3
) × I1
(5)
Voltages across each resistor can be calculated using voltage division rule as:
VR1 = (R
VR2 = (R
R1
1 +Req
Req
1 +Req
) × V1 ,
(6)
) × V1
(7)
And
VR2 = VR3
(8)
The above-mentioned equation is true since resistors R2 and R3 are in parallel and equal
value of voltage appears across them regardless of their values.
LAB SESSION
Lab task
Lay the circuit given below on bread board. Calculate as well as measure all the values of
voltages and currents using different laws.
Equipment and Materials
➢ Power supply
➢ Resistors
➢ Multi-meter
Experimental Procedure
1. Build the circuit as shown in the Fig.I1.
2. Use DMM to check continuity of the contact points of the circuit by setting DMM on
“continuity test mode” or
button to ensure proper connections of the circuit made.
3. Set the appropriate voltage by adjusting the Variable Power Supply (Vs) to 10 Volts.
4. Use the Digital Multi-Meter (DMM) to accurately measure all the voltages and currents in
the circuit. Record the measurements in Table 1.
5. Use formulas of Pre-Lab Task and calculate values of all voltages and currents in the
circuit. Record the results in Table 1 in respective columns.
6. Repeat Step 4 for measurements in Table 2.
7. Verify KVL for the loops in the circuit using equations 2a and 2b.
8. Verify KCL for the nodes in the circuit using equations 3a, 3b, 3c and 3d.
Hint: Use R1=56Ω, R2=390Ω and R3=100Ω.
Observations:
Table 1 Measurement of Resistance, Current and Voltage for Ohms Law
Resistance (kΩ)
Supply
Voltage
(V)
Current (I)
Calculated
R1
R2
Measured
Calculated
Measured
R3
I1
10
Voltage (V)
I2
I3
I1
I2
I3
V1
V2
V3
V1
V2
V3
5
15
Table 2 Measurement of Resistance, Current and Voltage for Kirchhoff’s Laws
Branch
voltage
Volts
Branch
Current
mA
Resistor
Vs
Is
V1
I1
R1
V2
I2
R2
V3
I3
R3
V4
I4
R4
V5
I5
R5
KΩ
LAB REPORT
Prepare the Lab Report as below:
TITLE:
OBJECTIVE:
APPARATUS:
PROCEDURE:
(Note: Use all steps you studied in PRE-LAB TASK & LAB SESSION of this tab to write
procedure and to complete the experiment)
RESULTS:
(Note: Use all Observation tables you studied in LAB SESSION of this lab to complete the
experiment)
DISCUSSION:
Questions
1. Write down the function and purpose of using a resistor in a circuit? Also, draw an
illustration of what a real resistor looks like.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
2. Resistors are often represented by a symbol given below in electrical and electronic
schematic diagrams but there is another symbol used for resistor representation.
Draw this other symbol ______________.
Conclusion /Summary
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
____________________________________________________________
Domains
Attributes
Psychomotor (70%)
Affective (20%)
Realization of
Experiment
Conducting
Experiment
Data
Collection
Data
Analysis
(Awareness)
(Act)
(Use
Instrument)
(Perform)
Taxonomy
Level
P1
P2
P2
Marks
distribution
3
5
3
Obtained
Marks
Discipline
Cognitive
(10%)
Apply
(Receiving)
Team work
(Respond/
Contribute)
P2
A1
A2
C3
3
2
2
2