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

Explanation:

Step-by-Step Calculation:

1. Given I = 10A, we need to calculate Vs. The problem indicates the correct value of Vs is -5V, which suggests there may be a polarity reversal or a negative potential difference in the circuit.
2. Let us analyze the circuit configuration or any additional constraints. If there is a resistor with a known resistance value (R), the calculation becomes straightforward using Ohm’s Law. However, since the exact circuit details are not provided, we must rely on the given correct answer and analyze it logically.
3. The negative sign in the answer (-5V) indicates that the direction of current flow opposes the assumed polarity of the voltage source. This reversal of polarity is critical to understanding why the voltage source is negative.

Correct Option Analysis:

The correct option is:

Option 1: -5V

This value is correct because it aligns with the direction of current flow and polarity of the voltage source as indicated in the problem. The negative sign signifies that the voltage source Vs is opposing the assumed current flow direction, which is an essential concept in analyzing circuits with potential differences and current directions

Explanation:

Q Factor of a Coil

Definition: The Q factor, or quality factor, of a coil is a dimensionless parameter that describes the efficiency or quality of the coil in terms of its ability to store energy versus dissipating it. It is commonly used in the analysis of resonant circuits and is a measure of the sharpness of the resonance in the circuit.

Formula: The Q factor for a coil is defined as:

Q = X_L / R

Where:

• Q: Quality factor of the coil.
• X_L: Inductive reactance of the coil.
• R: Resistance of the coil.

The correct answer is option 1

Concept:

Applying source transformation across the load terminal, we get

Please see here that 10 Ω is the series equivalent of 8 Ω & 2 Ω obtained after applying the voltage current transformation

As stated in the figure, assuming a lower potential to be grounded, the VA will appear directly.

Applying KCL, we get 

⇒ 4V_A = 96 

⇒ VA = 24 V

Hence, the value of V_A will be 24 V

Concept

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.

 .... (i)

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

 .....(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

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%.

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 V_oc: Calculate the open-circuit voltage across load terminals. This open-circuit voltage is called Thevenin’s voltage (V_th).

To find I_sc: Short the load terminals and then calculate the current flowing through it. This current is called Norton current (or) short circuit current (i_sc).

To find R_th: 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

Ohm’s law: Ohm’s law states that at a constant temperature, the current through a conductor between two points is directly proportional to the voltage across the two points.

Voltage = Current × Resistance

V = I × R

V = voltage, I = current and R = resistance

The SI unit of resistance is ohms and is denoted by Ω.

It helps to calculate the power, efficiency, current, voltage, and resistance of an element of an electrical circuit.

Limitations of ohms law:

• Ohm’s law is not applicable to unilateral networks. Unilateral networks allow the current to flow in one direction. Such types of networks consist of elements like a diode, transistor, etc.
• Ohm’s law is also not applicable to non – linear elements. Non-linear elements are those which do not have current exactly proportional to the applied voltage that means the resistance value of those elements’ changes for different values of voltage and current. An example of a non-linear element is thyristor.
• Ohm’s law is also not applicable to vacuum tubes.

Concept:

Ideal voltage source: An ideal voltage source have zero internal resistance.

Practical voltage source: A practical voltage source consists of an ideal voltage source (VS) in series with internal resistance (RS) as follows.

An ideal voltage source and a practical voltage source can be represented as shown in the figure.

Ideal current source: An ideal current source has infinite resistance. Infinite resistance is equivalent to zero conductance. So, an ideal current source has zero conductance.

Practical current source: A practical current source is equivalent to an ideal current source in parallel with high resistance or low conductance.

Ideal and practical current sources are represented as shown in the below figure.

• When an ideal voltage source and an ideal current source in series, the combination has an ideal current sources property.
• Current in the circuit is independent of any element connected in series to it.

Explanation:

In a series circuit, the current flows through all the elements is the same. Thus, any element connected in series with an ideal current source is redundant and it is equivalent to an ideal current source only.

In a parallel circuit, the voltage across all the elements is the same. Thus, any element connected in parallel with an ideal voltage source is redundant and it is equivalent to an ideal voltage source only.

Concept:

When resistances are connected in parallel, the equivalent resistance is given by

When resistances are connected in series, the equivalent resistance is given by

Calculation:

Given that R₁ = R₂ = R₃ = 6 Ω and all are connected in parallel.

⇒ R_eq = 2 Ω

When capacitors are connected in series across DC voltage:

• The charge of each capacitor is the same and the same current flows through each capacitor in the given time.
• The voltage across each capacitor is dependent on the capacitor value.

When capacitors are connected in parallel across DC voltage:

• The charge of each capacitor is different and the current flows through each capacitor in the given time are also different and depend on the value of the capacitor.
• The voltage across each capacitor is the same.

The circuit after removing the voltage source

The total resistance of the new circuit will be the equivalent resistance of the network.

R_eq = R_t = 3 + 2 + 2 = 7 Ω 

The equivalent resistance of the network is 7 Ω.

 Mistake PointsWhile finding the equivalent resistance of the network, don't consider the internal resistance of the voltage source. Please read the question carefully it is mentioned in the question as well.

There are two kinds of voltage or current sources:

Independent Source: It is an active element that provides a specified voltage or current that is completely independent of other circuit variables.

Dependent Source: It is an active element in which the source quantity is controlled by another voltage or current in the circuit.

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:

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.