Electrical Networks MCQ Quiz - Objective Question with Answer for Electrical Networks - Download Free PDF

Color Coding of Resistor

The value of the resistor is calculated as:

R = (First digit × 10 + Second digit) × 10^Multiplier

Calculation

Green = 5 (First digit)

Blue = 6 (Second digit)

Black = 0 (Multiplier = 10⁰ = 1)

Golden = ±5% (Tolerance)

R = (5 × 10 + 6) × 100

R = 56 Ω ± 5%

Fuse

• Fuse are designed to handle high fault currents and provide protection against short circuits and overloads in electrical systems. 
• A fuse is not a power-limiting device; instead, it is a current-limiting device designed to protect electrical circuits from excessive current.
• The fuse element inside a fuse is typically made from a high conductivity material, such as silver or copper. This element melts when excessive current flows through it, breaking the circuit.
• Fuse is consistent & it has the feature like if it has a high fault current then break time is low. Similarly, if the fault current is not high, then break time is long.
• In normal conditions, the flow of current through the fuse doesn’t provide sufficient energy to soften the element. If the huge current flows through the fuse then it melts the element of the fuse before the fault current achieves the climax.

A fuse protects circuits by breaking the connection when the current exceeds a safe limit, but it does not directly control or limit power consumption in normal operation. 

The correct answer is: 0.5 A

Key Points

• Maximum Current in AC Circuit:
  • The maximum current in a series RLC circuit is given by: I_max = V / R
  • Here, V = 6 V and I_max = 0.6 A
  • So, resistance R = V / I_max = 6 / 0.6 = 10 ohms
• Current through Coil with DC Cell:
  • Total resistance = resistance of coil + internal resistance of the cell
  • Given: resistance of coil = 10 ohms, internal resistance = 2 ohms
  • Total resistance = 10 + 2 = 12 ohms
  • Voltage from the cell = 6 V
  • So, current I = V / R_total = 6 / 12 = 0.5 A

Additional Information

• RLC Circuit in AC:
  • In AC, inductors and capacitors create reactance (opposition to current).
  • At resonance, inductive and capacitive reactances cancel out.
  • Only resistance (R) limits the current in that case.
• Ohm's Law:
  • Ohm's Law: I = V / R
  • This formula is used to find current when voltage and resistance are known.
  • It applies to both AC and DC circuits.

Magnetic Circuit

In a magnetic circuit, the force that tends to create magnetic flux is called MMF(magnetomotive force).

\(MMF=NI\)

where, N = No. of turns and I = Current

The SI unit of Magnetomotive force (MMF) is Ampere turn (AT).

Explanation:

SI Unit of Electrical Conductance: Siemens (S)

Definition: The Siemens (S) is the derived unit of electrical conductance in the International System of Units (SI). It is named after the German inventor and industrialist Ernst Werner von Siemens. Electrical conductance is the reciprocal of electrical resistance and represents how easily electricity flows through a material. The higher the conductance, the lower the resistance, and vice versa.

SI Base Units of Siemens (S):

To express Siemens in terms of SI base units, we start with its relationship to electrical resistance, which is measured in ohms (Ω). The SI unit of resistance, the ohm (Ω), is defined as one volt per ampere (Ω = V/A). Since conductance is the reciprocal of resistance, the unit of conductance (Siemens) is the reciprocal of the ohm.

Relationship: 1 S = 1 Ω^-1

In terms of SI base units, the ohm can be expressed as follows:

Ω = V/A

Where:

• V (volt) is the SI unit of electric potential, which can be expressed as kg m² s^-3 A^-1
• A (ampere) is the SI unit of electric current

Thus, the ohm can be rewritten in terms of SI base units:

Ω = kg m² s^-3 A^-1 / A

Simplifying this, we get:

Ω = kg m² s^-3 A^-2

Since Siemens (S) is the reciprocal of ohms (Ω), we take the reciprocal of the above expression:

1 S = (kg m² s^-3 A^-2)^-1

On taking the reciprocal, we get:

S = kg^-1 m^-2 s³ A²

This matches with Option 1. Therefore, the correct option is:

Option 1: kg^-1 m^-2 s³ A²

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 2: kg m² s^-3 A^-1

This option represents the SI base unit for voltage (V), not electrical conductance. The voltage can be expressed as kg m² s^-3 A^-1. Therefore, this option is incorrect.

Option 3: kg m² s^-3 A^-2

This option represents the SI base unit for electrical resistance (Ω), which is the reciprocal of electrical conductance. Therefore, this option is also incorrect.

Option 4: kg^-1 m² s³ A²

This option seems to be incorrect as it does not represent any standard physical quantity in SI base units correctly related to electrical conductance. It appears to be a misplaced expression.

Conclusion:

Understanding the SI base units for derived units like Siemens is crucial for accurately describing physical quantities in scientific and engineering contexts. The Siemens (S) is the unit of electrical conductance and is expressed in SI base units as kg^-1 m^-2 s³ A². This understanding helps in various applications, including electrical engineering and physics, where precise measurements and calculations of conductance are essential.

Concept:

The energy is given by:

\(E=P\times t\)

\(E=(V\times I)\times t\)

where, I = Current

R = Resistance

t = Time

Calculation:

Given, V = 220 V

E = 1.5 kW

t = 1 hr

\(1.5\times 10^3=220\times I\times 1\)

I = 6.82 A

The analogy between Electric Circuit and Magnetic Circuit:

Concept:

The resistance of conductor changes when the temperature of that conductor changes.

New resistance is given by:

\({{R}_{t}}={{R}_{0}}\left( 1+\alpha \text{ }\!\!\Delta\!\!\text{ }T \right)\)

Where Rt = Final resistance or the resistance of the conductor after temperature changes

R0 = Initial resistance or the resistance of the conductor before temperature changes

α = temperature coefficient 

ΔT = final temperature – initial temperature 

Calculation:

Given that

\({{R}_{t}}={{R}_{0}}\left( 1+\alpha \text{ }\!\!\Delta\!\!\text{ }T \right)\)

\(R_{20}\)= 1 Ω

α = 0.005 Ω/°C

T1 = 20°C

\(R_{20}\) = \(R_0\) (1+0.005 * \(10^{-3}\)(\(20-T_0\))}

\(R_{0}\)= 1.1\(\Omega\)

Now resistance

\({{R}_{t}}={{R}_{0}}\left( 1+\alpha \text{ }\!\!\Delta\!\!\text{ }T \right)\)

∴ 2 = \(\frac{1}{1.1}\) [1 + 0.005 × (T₂ - 20)]

T₂ * \(5\times10^{-3}\) = \(\frac{11}{5}-1\)

T₂ =240° C 

Dependent sources depend on some other quantity and these can be classified into four types:

1) Voltage Controlled Voltage Source (VCVS)

2) Voltage Controlled Current Source (VCCS)

3) Current Controlled Voltage Source (CCVS)

4) Current Controlled Current Source (CCCS)

The correct answer is option 4): (0.02/° C)

Concept:

The temperature coefficient of resistance is generally defined as the change in electrical resistance of a substance with respect to per degree change in temperature

R_T = R₀ [1+ α (∆T)]

 The change in electrical resistance of any substance due to temperature depends mainly on three factors –

1. The value of resistance at an initial temperature.
2. The rise in temperature.
3. The temperature coefficient of resistance α.

Calculation:

\(\frac{\Delta R}{R_0} = α × \Delta T\)

∆T = 20° C

R_T = \(140\over 100\) R0

∆R = RT - R0

=  \(140\over 100\) R0 - R0

= ​\(40\over 100\)R0

\(\frac{\Delta R}{R_0} = α × \Delta T\)

\(40\over 100\) = α × 20

α  = 0.02/° C

Passive Element:

• The element which receives or absorbs energy and then either converts it into heat (R) or stored it in an electric (C) or magnetic (L) field is called passive element
• Do not need any form of electrical power to operate
• Not able to control the flow of charge
• Cannot amplify, oscillate, or generate an electrical signal
• Used for energy storage, discharge, oscillating, filtering and phase shifting applications
• Examples: Resistor, inductor, capacitor

Important:

Active Element:

• The elements that supply energy to the circuit is called an active element
• These have an ability to control the flow of charge
• Used for current control and voltage control applications
• Examples: Battery, voltage source, current source, diode

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.

 ⇒ According to ohm's law, the Potential difference is directly proportional to the Current.

 ⇒ V œ I

 ⇒ V = IR ,where R is constant (Resistance)

⇒ V' =1/2 V then I' = 1/2 I

 ⇒ if the potential difference gets half then the current is also getting half.

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.

It an element follows the ohm’s law, then the element is known as a linear element.

Ex: Resistor

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.