Network Theorems MCQ Quiz - Objective Question with Answer for Network Theorems - Download Free PDF
Last updated on May 8, 2025
Latest Network Theorems MCQ Objective Questions
Network Theorems Question 1:
Find the voltage Vs in the circuit by using Kirchoff's Voltage Law.
Answer (Detailed Solution Below)
Network Theorems Question 1 Detailed Solution
Kirchhoff's Voltage Law (KVL)
According to KVL, the algebraic sum of the voltages in a closed loop is always zero.
ΣV = 0
Calculation
Applying KVL as per the direction ABCD:
+ 50 - 30 - VS - 10 + 20 = 0
VS = 30 V
Network Theorems Question 2:
A single-phase AC circuit has a voltage of 230 V and a current of 10 A. What is the apparent power (S)?
Answer (Detailed Solution Below)
Network Theorems Question 2 Detailed Solution
Apparent Power:
- Apparent power is the total power that appears to be transferred between the source and load in an AC circuit.
- It is given by S = VI
- The unit of apparent power is Volt-Amperes (VA).
Calculation
Given, V = 230 volts
I = 10 A
S = 230 × 10
S = 2300 VA = 2.3 kVA
Additional Information
Active Power:
- Active power is the real power consumed by the circuit.
- It is given by: P = VI cosϕ
- The unit of active power is watts (W).
Reactive Power:
- Reactive power is the electrical power that oscillates between the source and the load without performing useful work.
- It is given by P = VI sinϕ
- The unit of reactive power is Volt-Ampere Reactive (VAR).
Network Theorems Question 3:
In Norton’s Theorem, the equivalent circuit consists of _____.
Answer (Detailed Solution Below)
Network Theorems Question 3 Detailed Solution
Concept:
Norton’s Theorem states that any linear electrical network with voltage and current sources and resistors can be replaced at terminals A-B by an equivalent circuit consisting of a current source in parallel with a resistor.
Calculation
The Norton equivalent circuit includes: - Norton Current (IN): The short-circuit current through the output terminals. - Norton Resistance (RN): The equivalent resistance seen from the terminals when all independent sources are turned off. These two elements are connected in parallel.
Hence, the equivalent circuit consists of a current source in parallel with a resistor.
Network Theorems Question 4:
What is the Thevenins equivalent resistance at the terminals X, Y for the circuit shown in the figure?
Answer (Detailed Solution Below)
Network Theorems Question 4 Detailed Solution
Thevenin Theorem
Thevenin’s theorem states that it is possible to simplify any linear circuit, into an equivalent circuit with a single voltage source and a series resistance.
Steps to calculate:
- Thevenin Resistance (Rth): Open the circuit to the terminal from where the Thevenin resistance has to be found. While finding the Rth, short circuit the independent voltage source and open circuit the independent current source.
- Thevenin Voltage (Vth): This is the open-circuit voltage across the terminals where the load was connected.
Calculation
Open circuit the terminal XY to calculate Rth
3 kΩ, 1 kΩ and 2 kΩ are connected in series.
R = 3 + 2 + 1 = 6 kΩ
This 6 kΩ and 3 kΩ are connected in parallel.
RXY = 2 kΩ
Network Theorems Question 5:
In an electric circuit, the maximum power transferred to load resistance is 2Ω is 50 W. If now, the load resistance is changed to 8Ω, what will be the power transferred to the load?
Answer (Detailed Solution Below)
Network Theorems Question 5 Detailed Solution
Concept
The maximum power transfer theorem states that the maximum power is delivered to a load when the load resistance is equal to the source resistance.
The maximum power across the load is given by:
Now, the power transferred to the load at other loading condition is given by:
Calculation
Given, Pmax = 50 W at RL = Rth = 2Ω
Vth = 20V
P = 32 W
Top Network Theorems MCQ Objective Questions
A voltage source having some internal resistance delivers a 2A current when a 5Ω load is connected to it. When the load is 10Ω, then the current becomes 1.6A. Calculate the power transfer efficiency of the source for a 15Ω load.
Answer (Detailed Solution Below)
Network Theorems Question 6 Detailed Solution
Download Solution PDFConcept
The power transfer efficiency is:
The current across any resistor is given by:
where, I = Current
V = Voltage
R = Resistance
Calculation
Let the voltage and internal resistance of the voltage source be V and R respectively.
Case 1: When the current of 2 A flows through 5 Ω resistance.
Case 2: When the current of 1.6 A flows through 10 Ω resistance.
Solving equations (i) and (ii), we get:
2(5+R)=1.6(10+R)
10 + 2R = 16 + 1.6R
0.4R = 6
R = 15Ω
Putting the value of R = 15Ω in equation (i):
V = 40 volts
Case 3: Current when the load is 15Ω
η = 50%
Additional Information Condition for Maximum Power Transfer Theorem:
When the value of internal resistance is equal to load resistance, then the power transferred is maximum.
Under such conditions, the efficiency is equal to 50%.
As shown in the figure, a 1Ω resistance is connected across a source that has a load line V + i = 100. The current through the resistance is
Answer (Detailed Solution Below)
Network Theorems Question 7 Detailed Solution
Download Solution PDFConcept:
Thevenin's Theorem:
Any two terminal bilateral linear DC circuits can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.
To find Voc: Calculate the open-circuit voltage across load terminals. This open-circuit voltage is called Thevenin’s voltage (Vth).
To find Isc: Short the load terminals and then calculate the current flowing through it.
To find Rth: Since there are Independent sources in the circuit, we can’t find Rth directly. We will calculate Rth using Voc and Isc and it is given by
Application:
Given: Load line equation = V + i = 100
To obtain open-circuit voltage (Vth) put i = 0 in load line equation
⇒ Vth = 100 V
To obtain short-circuit current (isc) put V = 0 in load line equation
⇒ isc = 100 A
So,
Equivalent circuit is
Current (i) = 100/2 = 50 A
Applying loop-law in the given circuit.
- V + i × R = 0
- V + I × 1 = 0
⇒ V = i
Given Load line equation is V + i = 100
Putting V = i
then i + i = 100
⇒ i = 50 A
Which of the following statements are true for KCL and KVL
(a) Valid for distributed parameters networks
(b) Valid for lumped parameters networks
(c) Valid for linear elements
(d) Valid for non-linear elements
Code:
Answer (Detailed Solution Below)
Network Theorems Question 8 Detailed Solution
Download Solution PDFDistributed Network:
- If the network element such as resistance, capacitance, and inductance are not physically separated, then it is called a Distributed network.
- Distributed systems assume that the electrical properties R, L, C, etc. are distributed across the entire circuit.
- These systems are applicable for high (microwave) frequency applications.
Lumped Network:
- If the network element can be separated physically from each other, then they are called a lumped network.
- Lumped means a case similar to combining all the parameters and considering it as a single unit.
- Lumped systems are those systems in which electrical properties like R, L, C, etc. are assumed to be located on a small space of the circuit.
- These systems are applicable to low-frequency applications.
Kirchoff's Laws:
- Kirchhoff’s laws are used for voltage and current calculations in electrical circuits.
- These laws can be understood from the results of the Maxwell equations in the low-frequency limit.
- They are applicable for DC and AC circuits at low frequencies where the electromagnetic radiation wavelengths are very large when we compare with other circuits. So they are only applicable for lumped parameter networks.
Kirchhoff's current law (KCL) is applicable to networks that are:
- Unilateral or bilateral
- Active or passive
- Linear or non-linear
- Lumped network
KCL (Kirchoff Current Law): According to Kirchhoff’s current law (KCL), the algebraic sum of the electric currents meeting at a common point is zero.
Mathematically we can express this as:
Where in represents the nth current
M is the total number of currents meeting at a common node.
KCL is based on the law of conservation of charge.
Kirchhoff’s Voltage Law (KVL):
It states that the sum of the voltages or electrical potential differences in a closed network is zero.
According to Tellegen's Theorem, the sum of instantaneous powers for the n branches in a network is always:
Answer (Detailed Solution Below)
Network Theorems Question 9 Detailed Solution
Download Solution PDF- According to Tellegen’s theorem, the summation of instantaneous powers for the n number of branches in an electrical network is zero.
- Let n number of branches in an electrical network have I1, I2, I3, ….. In respective instantaneous currents through them.
- These branches have instantaneous voltages across them are V1, V2, V3, ….. Vn respectively.
- According to Tellegen’s theorem,
- It is based on the conservation of energy.
- It is applicable to both linear and non-linear circuits.
Consider the following network
Suppose Va = 60 V and R is adjustable then find the value of 'R' such that maximum power is transferred through network N2 from network N1
Answer (Detailed Solution Below)
Network Theorems Question 10 Detailed Solution
Download Solution PDFConcept:
Maximum power transfer theorem:
Maximum power transfer theorem states that " In a linear bilateral network if the entire network is represented by its Thevenin's equivalent circuit then the maximum power transferred from source to the load when the load impedance is equal to the complex conjugate of Thevenin's impedance.
Let's consider variable resistive load and Thevenin's equivalent network as shown below,
Where,
Pm is the maximum power
Vth is the source voltage or Thevenin's voltage
Rth is the Thevenin's resistance (Rth = RL = RS)
The efficiency of the maximum power transfer theorem will be 50 %
The voltage across the load resistance/impedance is VL = VS / 2
Calculation:
Given the circuit diagram
Source voltage VS = 200 V
Va = 60 V
As V is the voltage across the load.
V = VS / 2 = 200 / 2 = 100 V
Load current i = V / RL (When maximum power is transferred RL = RS = Rth = 10 Ω)
i = 100 / 10 = 10 A
By applying nodal analysis at node V
R = 8 Ω
Therefore, the value of R is 8 Ω when Va is 60 V and maximum power is transferred from N1 to N2
Calculate current I in the following circuit using superposition theorem.
Answer (Detailed Solution Below)
Network Theorems Question 11 Detailed Solution
Download Solution PDFConcept:
Superposition theorem is used to solve a circuit that contains multiple current and/or voltage sources acting together.
Theorem:
- The superposition theorem states that "in a linear circuit with several sources, the current and voltage for any element in the circuit is the sum of the currents and voltages produced by each source acting independently."
- The superposition theorem applies only when all the components of the circuit are linear, which is the case for resistors, capacitors, and inductors it is not applicable to networks containing nonlinear elements.
Calculation:
case 1:
When 8 V source are there
I = 8 / 16 = 0.5 A
case 2:
When only 2 A current source present
Apply KVL in loop
6 I + 2 ( I - 2 )+ 8 I = 0
I = 0.25 A
case 3:
When 6 V source are there
I = - 6 / 16 = - 0.375 A
Now using superposition theorem
Total current I = 0.5 + 0.25 + ( - 0.375 ) A
= 0.375 A
= 375 mA
Important Points
Various Theorem and the circuits where they are applicable is shown below in the table:
Theorem |
Applicability |
Superposition Theorem |
Linear |
Thevenin Theorem |
Linear |
Norton Theorem |
Linear |
Maximum Power Transfer |
Linear |
Tellegen |
All |
Substitution |
Linear and Non-Linear |
A DC voltage source has a source resistance variable from 5 Ω to 25 Ω and it is connected to a load of 10 Ω. For maximum power transfer, the source resistance should be:
Answer (Detailed Solution Below)
Network Theorems Question 12 Detailed Solution
Download Solution PDFConcept:
Maximum power transfer theorem:
- Maximum power transfer theorem states that " In a linear bilateral network if the entire network is represented by its Thevenin's equivalent circuit then the maximum power transferred from source to the load when the load resistance is equal to the Thevenin's resistance."
"> P=VS2.RL(RS+RL)2" role="presentation" style="display: inline; position: relative;" tabindex="0">P=VS2.RL(RS+RL)2For maximum power transfer, RL = Rth- Then the maximum power transferred is given by
Explanation:
Circuit Diagram
Given,
Rs = 5 to 25 Ω (variable)
RL = 10 Ω (fixed)
Here Maximum Power Transfer theorem is not applicable as the load resistor is not variable.
Current,
Power transferred to load RL,
It is clear that for P to be maximum, RS should be minimum.
∴ RS = 5 Ω
Additional Information
Properties of maximum power transfer theorem:
- This theorem is applicable only for linear networks i.e networks with R, L, C, transformer, and linear controlled sources as elements.
- The presence of dependent sources makes the network active and hence, MPPT is used for both active as well as passive networks.
- This theorem is applicable when the load is variable.
Maximum power transfers at RL = Rs
The current at this condition is,
The maximum value of current occurs at RL = 0 and is given by
Therefore, the current at maximum power is equal to 50% of the maximum current
Key Points
- If source impedance is complex then load impedance has to be a complex conjugate of source impedance for maximum power transfer to occur.
- Maximum efficiency is not related to maximum power transfer.
Reciprocity theorem cannot be applied to the circuits having ______.
Answer (Detailed Solution Below)
Network Theorems Question 13 Detailed Solution
Download Solution PDFReciprocity theorem:
Reciprocity theorem states that in any branch of a network, the current (I) due to a single source of voltage (V) elsewhere in the network is equal to the current through the branch in which the source was originally placed when the source is placed in the branch in which the current (I) was originally obtained.
In the circuit (a), the value Ia is obtained for a voltage source V. According to reciprocity theorem, this current is equivalent to Ib in the circuit B.
Limitations of reciprocity theorem:
- The network should be bilateral linear and time-invariant.
- It can apply only to the single-source network and not for multi-source.
- It is also applicable for passive networks consisting L,C.
- Not applicable for circuits containing dependent sources even if it is linear.
Determine the load resistance RL that will result in maximum power delivered to the load for the given circuit. Also, determine the maximum power Pmax delivered to the load resistor.
Answer (Detailed Solution Below)
Network Theorems Question 14 Detailed Solution
Download Solution PDFConcept:
Maximum power transfer for DC circuit:
According to the MPT the maximum power transfer to the load when the load resistance is equal to the source resistance or Thevenin resistance.
RL = Rth
RL = load resistance
Rth = Thevenin or source resistance
The power at maximum power transfer (Pmax) = Vth2 / 4Rth
The maximum power transfer theorem is used in electrical circuits.
Calculation:
Rth = RL
= ( 30 × 150 ) / 180
= 25 Ω
Vth = Vab
= ( 150 × 180 ) / (150 + 30 )
= 150 V
From above concept,
Pmax = 225 W
Reciprocity theorem is applicable to a network
1. Containing R, L and C elements
2. Which is initially not a relaxed system
3. Having both dependent and independent sources
Which of the above is/are correct?
Answer (Detailed Solution Below)
Network Theorems Question 15 Detailed Solution
Download Solution PDFReciprocity theorem: It states that the current I in any branch of a network, due to single voltage source (E) anywhere in the network is equal to the current of the branch in which source was placed originally and when the source is again put in the branch in which current is obtained originally.
Limitations of reciprocity theorem:
- The network should be linear and time-invariant
- It can apply only to the single-source network