Network Theorems MCQ Quiz - Objective Question with Answer for Network Theorems - Download Free PDF

Last updated on Jun 25, 2025

Latest Network Theorems MCQ Objective Questions

Network Theorems Question 1:

Norton equivalent current source and corresponding resistance for the given circuit are respectively

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  1. 0.4A, 10 Ω
  2. 1.5 Α, 10 Ω
  3. 0.4 A, 4 Ω
  4. 1.5 Α, 4 Ω

Answer (Detailed Solution Below)

Option 1 : 0.4A, 10 Ω

Network Theorems Question 1 Detailed Solution

Explanation:

Norton Equivalent Current Source and Resistance:

In electrical circuit analysis, the Norton equivalent of a network is a simplified representation that consists of a single current source (Norton current source, IN) in parallel with a single resistance (Norton resistance, RN). This simplification is especially useful for analyzing complex circuits and determining current through or voltage across specific components.

To calculate the Norton equivalent for a given circuit, the following steps are performed:

  1. Determine the Norton current (IN): This is the current through the terminals of the circuit when they are short-circuited.
  2. Determine the Norton resistance (RN): This is the equivalent resistance of the circuit seen from the terminals with all independent sources turned off (voltage sources shorted and current sources opened).

Let us now analyze the problem step-by-step and calculate the Norton equivalent current source and resistance for the given circuit.

Step 1: Norton Current (IN)

To find the Norton current, we need to short-circuit the output terminals of the given circuit and calculate the current through the short circuit. For the given problem, after performing the necessary circuit analysis (such as applying Ohm’s Law, Kirchhoff’s Voltage Law, or Kirchhoff’s Current Law), the value of the Norton current is found to be:

IN = 0.4 A

Step 2: Norton Resistance (RN)

The Norton resistance is determined by calculating the equivalent resistance of the circuit as seen from the output terminals with all independent sources turned off:

  • Voltage sources: Replaced by short circuits.
  • Current sources: Replaced by open circuits.

After simplifying the given circuit appropriately, the equivalent resistance is calculated to be:

RN = 10 Ω

Final Norton Equivalent:

The Norton equivalent circuit for the given circuit is:

  • Norton current source (IN): 0.4 A
  • Norton resistance (RN): 10 Ω

Thus, the correct answer is:

Option 1: 0.4 A, 10 Ω

Network Theorems Question 2:

For a given passive linear network, the Thevenin equivalent circuit series resistance and Norton equivalent circuit parallel resistance are respectively RTH and RN. Which of the following is true

  1. (RTH, RN) = (0, ∞)
  2. (RTH, RN) = (∞, 0)
  3. RTH RN
  4. RTH = RN

Answer (Detailed Solution Below)

Option 4 : RTH = RN

Network Theorems Question 2 Detailed Solution

Explanation:

Analysis of Thevenin and Norton Equivalent Circuits

Definition: Thevenin and Norton equivalent circuits are techniques used in electrical engineering to simplify complex networks into more manageable forms for analysis. Thevenin's theorem represents a network as an ideal voltage source (VTH) in series with a resistance (RTH), while Norton’s theorem represents the same network as an ideal current source (IN) in parallel with a resistance (RN).

Key Relationship:

The resistances RTH (Thevenin resistance) and RN (Norton resistance) are always equal in value:

RTH = RN

This equivalence arises because both Thevenin and Norton transformations describe the same electrical network, but in different forms. The resistance remains unchanged during the transformation, as it represents the inherent impedance of the circuit.

Correct Option Analysis:

The correct option is:

Option 4: RTH = RN

This option is correct because the Thevenin equivalent resistance (RTH) and Norton equivalent resistance (RN) of a given passive linear network are always equal. This fundamental relationship ensures consistency in circuit transformations and analysis.

Network Theorems Question 3:

A voltage source having source impedance of 10 ohm in series with 10 mH inductance generates a sinusoidal signal of amplitude 10 V and angular frequency 10 rad/s. What should be the load to get the maximum power transferred?

  1. 10 Ω resistance
  2. 10 Ω in series with 10 mH inductance
  3. 10 Ω in series with 1F capacitance
  4. 10 Ω in series with 10 mF capacitance

Answer (Detailed Solution Below)

Option 3 : 10 Ω in series with 1F capacitance

Network Theorems Question 3 Detailed Solution

Explanation:

To achieve maximum power transfer, the load impedance must match the complex conjugate of the source impedance. In this problem, the source impedance is given as 10 Ω in series with 10 mH inductance. The complex impedance of the source can be expressed as:

Zsource = R + jωL

Here:

  • R = 10 Ω (resistance)
  • L = 10 mH = 0.01 H (inductance)
  • ω = 10 rad/s (angular frequency)

Substituting the values:

Zsource = 10 + j(10 × 0.01) = 10 + j0.1 Ω

The complex conjugate of the source impedance is:

Zload = R - jωL = 10 - j0.1 Ω 

To match this impedance, the load should consist of a 10 Ω resistor in series with a capacitive reactance that cancels out the inductive reactance of the source. The capacitive reactance is given by:

XC = -XL = -ωL

XC = -0.1 Ω

The reactance of a capacitor is related to its capacitance by the formula:

XC = 1 / (ωC)

Substituting the values:

-0.1 = 1 / (10 × C)

C = 1 / (10 × 0.1) = 1 F

Thus, the load impedance that matches the complex conjugate of the source impedance is a 10 Ω resistor in series with a 1 F capacitor. Therefore, the correct answer is Option 3.

Network Theorems Question 4:

A circuit component consists of a resistor in parallel with an ideal current source. The I-V characteristics of the component was measured using a variable voltage source and an ammeter ' 𝐴 '.
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The arrow in the figure indicates the positive direction of current. The I-V characteristics of the component is best represented by

  1. qImage682c59428ef8145dab0b92cb
  2. qImage682c59438ef8145dab0b92cd
  3. qImage682c59438ef8145dab0b92cf
  4. qImage682c59438ef8145dab0b92d0

Answer (Detailed Solution Below)

Option 2 : qImage682c59438ef8145dab0b92cd

Network Theorems Question 4 Detailed Solution

Calculation:

Using Kirchhoff rule 

V = (I + Io ) R 

⇒ I = V/R - I0

at V =0 ⇒ I = - Io

at I = 0 ⇒ V = I0 R

Thus only correct graph is 

qImage682c59438ef8145dab0b92cd

Network Theorems Question 5:

Find the voltage Vs in the circuit by using Kirchoff's Voltage Law. 

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  1. 10 V
  2. 20 V
  3. 30 V
  4. 50 V

Answer (Detailed Solution Below)

Option 3 : 30 V

Network Theorems Question 5 Detailed Solution

Kirchhoff's Voltage Law (KVL)

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According to KVL, the algebraic sum of the voltages in a closed loop is always zero.

ΣV = 0

V1+V2+V3+V4=0

Calculation

Applying KVL as per the direction ABCD:

+ 50 - 30 - VS - 10 + 20 = 0

VS = 30 V

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.

  1. 90%
  2. 50%
  3. 100%
  4. 10%

Answer (Detailed Solution Below)

Option 2 : 50%

Network Theorems Question 6 Detailed Solution

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Concept

The power transfer efficiency is:

η=I2RLVI×100

η=IRLV×100

The current across any resistor is given by:

I=VR

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.

2=V5+R .... (i)

Case 2: When the current of 1.6 A flows through 10 Ω resistance.

1.6=V10+R .....(ii)

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

I=VR+RL

I=4015+15=43A

η=43×1540×100

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

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  1. 25 A
  2. 50 A
  3. 100 A
  4. 200 A

Answer (Detailed Solution Below)

Option 2 : 50 A

Network Theorems Question 7 Detailed Solution

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Concept:

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. This current is called Norton current (or) short circuit current (isc).

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

Rth=Vocisc  

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, Rth=Vthisc=100100=1Ω

Equivalent circuit is

Gate EE NETWORK 1 mobile-Images-Q51.1

Current (i) = 100/2 = 50 A

 

Applying loop-law in the given circuit.

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- 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:

  1. (b) and (c)
  2. (a), (b) and (c)
  3. (b), (c) and (d)
  4. (a), (c) and (d)

Answer (Detailed Solution Below)

Option 3 : (b), (c) and (d)

Network Theorems Question 8 Detailed Solution

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Distributed 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:

n=1Min=0

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:

  1. Constant
  2. Equal to zero
  3. In-phase with current
  4. Alternating

Answer (Detailed Solution Below)

Option 2 : Equal to zero

Network Theorems Question 9 Detailed Solution

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  • 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, k=1nVk.Ik=0
  • It is based on the conservation of energy.
  • It is applicable to both linear and non-linear circuits.

Consider the following network

F1 Vijay 19-02-21 Savita D4

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

  1. 7 Ω
  2. 8 Ω
  3. 9 Ω
  4. 10 Ω

Answer (Detailed Solution Below)

Option 2 : 8 Ω

Network Theorems Question 10 Detailed Solution

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Concept:

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,

F1 Jai 9.11.20 Pallavi D1 

Pm=Vth24Rth

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

F1 Vijay 19-02-21 Savita D4

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

i+V20+VVaR=0

10+10020+10060R=0

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.

F1 Shubham Madhuri 11.05.2021 D12

  1. 375 mA
  2. 200 mA
  3. 150 mA
  4. 100 mA

Answer (Detailed Solution Below)

Option 1 : 375 mA

Network Theorems Question 11 Detailed Solution

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Concept:

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

F1 Shubham Madhuri 11.05.2021 D13

I = 8 / 16 = 0.5 A

case 2:

When only 2 A current source present

F1 Shubham Madhuri 11.05.2021 D14

Apply KVL in loop

6 I + 2 ( I - 2 )+ 8 I = 0

I = 0.25 A

case 3:

When 6 V source are there

F1 Shubham Madhuri 11.05.2021 D15

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:

  1. 5 Ω 
  2. 10 Ω 
  3. 15 Ω 
  4. 25 Ω 

Answer (Detailed Solution Below)

Option 1 : 5 Ω 

Network Theorems Question 12 Detailed Solution

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Concept:

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 Pmax=VS24RL

Explanation:

Circuit Diagram

F1 Nakshatra Anil 14-06.21 D2

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, I=VRs+RL

Power transferred to load RL,

P=I2RL=[VRS+RL]2×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,

IL=VS2RL=VS2RS

The maximum value of current occurs at R = 0 and is given by
IL=VRS

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 ______.

  1. Linear elements
  2. Dependent sources
  3. Bilateral elements
  4. Passive elements

Answer (Detailed Solution Below)

Option 2 : Dependent sources

Network Theorems Question 13 Detailed Solution

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Reciprocity 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.

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In the circuit (a), the value Iis 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.

F1 ENG Savita 12-04-24 D1 V2

  1. RL = 50 Ω; Pmax = 225 W
  2. RL = 35 Ω; Pmax = 200 W
  3. RL = 20 Ω; Pmax = 200 W
  4. RL = 25 Ω; Pmax = 225 W

Answer (Detailed Solution Below)

Option 4 : RL = 25 Ω; Pmax = 225 W

Network Theorems Question 14 Detailed Solution

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Concept:

Maximum power transfer for DC circuit:

F1 Jai 9.11.20 Pallavi D1

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:

F1 Ravi Ranjan Ravi 10.05.21 D1

Rth = RL

= ( 30 × 150 )  / 180

= 25 Ω 

F1 Ravi Ranjan Ravi 10.05.21 D2

Vth = Vab 

= ( 150 × 180 ) / (150 + 30 )

= 150 V

From above concept,

Pmax=Vth24Rth=15024×25=225 W

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?

  1. 1 only
  2. 1 and 2 only
  3. 2 and 3 only
  4. 1, 2 and 3

Answer (Detailed Solution Below)

Option 1 : 1 only

Network Theorems Question 15 Detailed Solution

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Reciprocity 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
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