Admittance MCQ Quiz - Objective Question with Answer for Admittance - Download Free PDF

Explanation:

In electrical engineering, the concept of admittance is crucial for analyzing and understanding AC circuits. Admittance is the measure of how easily a circuit or a component allows the flow of electric current when a voltage is applied. It is the reciprocal of impedance. In this detailed explanation, we will delve into the concept of admittance, its relationship with impedance, and why it is the correct answer among the given options.

Admittance:

Admittance (Y) is defined as the reciprocal of impedance (Z). Mathematically, it is expressed as:

Y = 1 / Z

Where:

• Y is the admittance, measured in Siemens (S).
• Z is the impedance, measured in Ohms (Ω).

Impedance is a complex quantity that combines resistance (R) and reactance (X) in an AC circuit. It is given by:

Z = R + jX

Where:

• R is the resistance, representing the real part of impedance.
• X is the reactance, representing the imaginary part of impedance.
• j is the imaginary unit (√-1).

Admittance, being the reciprocal of impedance, is also a complex quantity and can be expressed as:

Y = G + jB

Where:

• G is the conductance, representing the real part of admittance.
• B is the susceptance, representing the imaginary part of admittance.

Conductance (G) is the reciprocal of resistance (R), and susceptance (B) is the reciprocal of reactance (X). Therefore, admittance provides a comprehensive measure of how easily current flows through a circuit, considering both resistance and reactance.

Why Option 4 is Correct:

Option 4 states that admittance is the reciprocal of impedance. This is the correct answer because, by definition, admittance (Y) is the measure of how easily a circuit or component allows the flow of electric current, and it is mathematically defined as the reciprocal of impedance (Z). Understanding this relationship is fundamental in AC circuit analysis and helps engineers design and analyze circuits more effectively.

To further illustrate this concept, let's consider an example:

Example:

Suppose we have an AC circuit with an impedance of Z = 4 + j3 Ω. To find the admittance, we take the reciprocal of the impedance:

Y = 1 / Z

To calculate the reciprocal of a complex number, we multiply the numerator and denominator by the complex conjugate of the denominator:

Y = 1 / (4 + j3) × (4 - j3) / (4 - j3)

Simplifying this, we get:

Y = (4 - j3) / ((4 + j3) × (4 - j3))

Y = (4 - j3) / (16 + 9)

Y = (4 - j3) / 25

Y = 0.16 - j0.12 S

So, the admittance of the circuit is 0.16 - j0.12 Siemens. This result shows how the real part (conductance) and the imaginary part (susceptance) of admittance provide insight into the behavior of the circuit.

Additional Information

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

Option 1: Inductance

Inductance (L) is a property of an electrical conductor or circuit that causes it to oppose a change in the current flowing through it. It is not directly related to admittance. Inductance is measured in Henrys (H) and is associated with the storage of energy in a magnetic field. Therefore, admittance is not the reciprocal of inductance.

Option 2: Resistance

Resistance (R) is a measure of how much a component or circuit resists the flow of electric current. It is measured in Ohms (Ω) and represents the real part of impedance. While conductance (G) is the reciprocal of resistance, admittance is the reciprocal of impedance, which includes both resistance and reactance. Therefore, admittance is not simply the reciprocal of resistance.

Option 3: Capacitor

A capacitor is a passive electronic component that stores electrical energy in an electric field. It is characterized by its capacitance (C), measured in Farads (F). Capacitance is not directly related to admittance. Admittance is a broader concept that encompasses the ease of current flow in an AC circuit, considering both resistance and reactance. Therefore, admittance is not the reciprocal of a capacitor.

Conclusion:

Understanding the concept of admittance and its relationship with impedance is essential for analyzing and designing AC circuits. Admittance is the reciprocal of impedance, providing a comprehensive measure of how easily current flows through a circuit. This relationship is fundamental in electrical engineering and helps engineers effectively analyze and design circuits. While the other options (inductance, resistance, and capacitor) are important electrical properties and components, they are not directly related to the definition of admittance. Therefore, the correct answer is option 4: impedance.

Concept:

Impedance (Z) = \({1\over Admittance (Y)}\)

Z = R + jX

where, R = Resistance & X = Reactance

Y = G + jB

where, G = Conductance & B = Susceptance

Calculation:

Given, Y = 3 + j4

\(Z={1\over 3+j4}\)

\(Z={1\over 3+j4}\times{3-j4\over 3-j4}\)

\(Z={1\over 25}(3-j4)\)

Resistance, R = \(\frac{3}{25}\Omega\)

The correct answer is option 1):(Z = 12 + j16 Ω )

Concept:

Admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance,

Z = \(1 \over Y\)

Calculation:

Given

Y = 0.03 - j0.04 siemen

Z = \(1 \over Y\)

= \(1 \over 0.03 - j0.04 \)

Z = 12 + j16 Ω 

The correct answer is option 4):(Y = 0.24 - j0.06 mho)

Concept:

Admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance,

Z = \(1 \over Y\)

When two admittance connected in parallel then admittance

Y = Y₁ + Y₂

Calculation:

Given 

 Z1 = (4 + j3) Ω 

Y₁ = \(1\over Z_1\)

=\(1 \over 4+j3\)

= \(0.16 -0.12 i\)

Z2 = (8 - j6) Ω 

Y₂ = \(1 \over Z_2\)

= \( 1\over (8 - j6)\)

= 0.08 + 0.06i 

Y = Y1 + Y2

= 0.08 + 0.06i + \(0.16 -0.12 i\)

=  0.24 - j0.06 mho

Concept

The relationship between impedance and admittance is given by:

\(Y={1\over Z}\)

where, Y = Admittance

Z = Impedance

Calculation

Given, Z = 3 + j4

\(Y={1\over 3+j4}\times {3-j4\over 3-j4}\)

\(Y={3-j4\over (3)^2\space +(4)^2}\)

\(Y={3-j4\over 25}\)

Y = 0.12 − j0.16

Concept

The relationship between impedance and admittance is given by:

\(Y={1\over Z}\)

where, Y = Admittance

Z = Impedance

Calculation

Given, Z = 3 + j4

\(Y={1\over 3+j4}\times {3-j4\over 3-j4}\)

\(Y={3-j4\over (3)^2\space +(4)^2}\)

\(Y={3-j4\over 25}\)

Y = 0.12 − j0.16

Concept:

Impedance (Z) = \({1\over Admittance (Y)}\)

Z = R + jX

where, R = Resistance & X = Reactance

Y = G + jB

where, G = Conductance & B = Susceptance

Calculation:

Given, Y = 3 + j4

\(Z={1\over 3+j4}\)

\(Z={1\over 3+j4}\times{3-j4\over 3-j4}\)

\(Z={1\over 25}(3-j4)\)

Resistance, R = \(\frac{3}{25}\Omega\)

The correct answer is option 4):(Y = 0.24 - j0.06 mho)

Concept:

Admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance,

Z = \(1 \over Y\)

When two admittance connected in parallel then admittance

Y = Y₁ + Y₂

Calculation:

Given 

 Z1 = (4 + j3) Ω 

Y₁ = \(1\over Z_1\)

=\(1 \over 4+j3\)

= \(0.16 -0.12 i\)

Z2 = (8 - j6) Ω 

Y₂ = \(1 \over Z_2\)

= \( 1\over (8 - j6)\)

= 0.08 + 0.06i 

Y = Y1 + Y2

= 0.08 + 0.06i + \(0.16 -0.12 i\)

=  0.24 - j0.06 mho

The correct answer is option 1):(Z = 12 + j16 Ω )

Concept:

Admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance,

Z = \(1 \over Y\)

Calculation:

Given

Y = 0.03 - j0.04 siemen

Z = \(1 \over Y\)

= \(1 \over 0.03 - j0.04 \)

Z = 12 + j16 Ω 

The relationship between the impedance and admittance is given by:

\(Z= {1\over Y}\)

where Z = Impedance

Y = Admittance

The impedance is analogous to admittance in the following ways:

Admittance (Y):

The admittance of an AC circuit is defined as the reciprocal of its impedance (Z) i.e.

\(Y=\frac{1}{Z}=\frac{I}{V}\)

The unit of admittance is siemens (S).

Impedance (Z) is the opposition to alternating current flow, admittance (Y) is the inducement to alternating current flow.

Components of Admittance:

Depending upon the nature of reactance, the impedance of an AC circuit can be expressed in the complex form as :

Z = R + j X_L

or, Z = R – j X_C

Here, R is the resistive or in-phase component of Z while X_L or X_C is the reactive or quadrature component of Z.

Using Admittance Triangle,

or,

From the above triangle,

G = \(\frac{R}{Z^2}\)

B_c = \(\frac{X_c}{Z^2}\)

B_L = \(\frac{X_L}{Z^2}\)

Hence, Y = G ± j (B_c - B_L)

Explanation:

Resistance

It is an electrical parameter that is used as the measurement of opposition to the electric current.

The reciprocal of the resistance is called the 'Admittance'.

Resistance is defined as:

\(R=\frac{ρ l}{A}\)

ρ: Resistivity of the material

l: length of the conductor

A: Area of the cross-section of the conductor.

It is measured in Ω.

Impedance:

The complex quantity of the resistance is defined as the Impedance of a circuit. 

It is the same as that of the resistance.

Admittance

It is defined as the parameter which is used to measure the flow of current easily in a circuit.

\(admitatance=\frac{1}{resistance}\)

It is measured in Ω^-1 or Siemens(S).

From Ohm's law admittance is:

\(Admittance = \frac{I}{V}\)

Capacitance

It is an electrical element that stores energy in the form of a static electric charge.

Energy stored in a capacitor is:

\(E=\frac{1}{2}CV^2\)

V: Voltage across the capacitor.

SI unit is Farads. (F)

Conclusion:

Option 2 is correct.

Explanation:

In electrical engineering, the concept of admittance is crucial for analyzing and understanding AC circuits. Admittance is the measure of how easily a circuit or a component allows the flow of electric current when a voltage is applied. It is the reciprocal of impedance. In this detailed explanation, we will delve into the concept of admittance, its relationship with impedance, and why it is the correct answer among the given options.

Admittance:

Admittance (Y) is defined as the reciprocal of impedance (Z). Mathematically, it is expressed as:

Y = 1 / Z

Where:

• Y is the admittance, measured in Siemens (S).
• Z is the impedance, measured in Ohms (Ω).

Impedance is a complex quantity that combines resistance (R) and reactance (X) in an AC circuit. It is given by:

Z = R + jX

Where:

• R is the resistance, representing the real part of impedance.
• X is the reactance, representing the imaginary part of impedance.
• j is the imaginary unit (√-1).

Admittance, being the reciprocal of impedance, is also a complex quantity and can be expressed as:

Y = G + jB

Where:

• G is the conductance, representing the real part of admittance.
• B is the susceptance, representing the imaginary part of admittance.

Conductance (G) is the reciprocal of resistance (R), and susceptance (B) is the reciprocal of reactance (X). Therefore, admittance provides a comprehensive measure of how easily current flows through a circuit, considering both resistance and reactance.

Why Option 4 is Correct:

Option 4 states that admittance is the reciprocal of impedance. This is the correct answer because, by definition, admittance (Y) is the measure of how easily a circuit or component allows the flow of electric current, and it is mathematically defined as the reciprocal of impedance (Z). Understanding this relationship is fundamental in AC circuit analysis and helps engineers design and analyze circuits more effectively.

To further illustrate this concept, let's consider an example:

Example:

Suppose we have an AC circuit with an impedance of Z = 4 + j3 Ω. To find the admittance, we take the reciprocal of the impedance:

Y = 1 / Z

To calculate the reciprocal of a complex number, we multiply the numerator and denominator by the complex conjugate of the denominator:

Y = 1 / (4 + j3) × (4 - j3) / (4 - j3)

Simplifying this, we get:

Y = (4 - j3) / ((4 + j3) × (4 - j3))

Y = (4 - j3) / (16 + 9)

Y = (4 - j3) / 25

Y = 0.16 - j0.12 S

So, the admittance of the circuit is 0.16 - j0.12 Siemens. This result shows how the real part (conductance) and the imaginary part (susceptance) of admittance provide insight into the behavior of the circuit.

Additional Information

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

Option 1: Inductance

Inductance (L) is a property of an electrical conductor or circuit that causes it to oppose a change in the current flowing through it. It is not directly related to admittance. Inductance is measured in Henrys (H) and is associated with the storage of energy in a magnetic field. Therefore, admittance is not the reciprocal of inductance.

Option 2: Resistance

Resistance (R) is a measure of how much a component or circuit resists the flow of electric current. It is measured in Ohms (Ω) and represents the real part of impedance. While conductance (G) is the reciprocal of resistance, admittance is the reciprocal of impedance, which includes both resistance and reactance. Therefore, admittance is not simply the reciprocal of resistance.

Option 3: Capacitor

A capacitor is a passive electronic component that stores electrical energy in an electric field. It is characterized by its capacitance (C), measured in Farads (F). Capacitance is not directly related to admittance. Admittance is a broader concept that encompasses the ease of current flow in an AC circuit, considering both resistance and reactance. Therefore, admittance is not the reciprocal of a capacitor.

Conclusion:

Understanding the concept of admittance and its relationship with impedance is essential for analyzing and designing AC circuits. Admittance is the reciprocal of impedance, providing a comprehensive measure of how easily current flows through a circuit. This relationship is fundamental in electrical engineering and helps engineers effectively analyze and design circuits. While the other options (inductance, resistance, and capacitor) are important electrical properties and components, they are not directly related to the definition of admittance. Therefore, the correct answer is option 4: impedance.

Concept

The relationship between impedance and admittance is given by:

\(Y={1\over Z}\)

where, Y = Admittance

Z = Impedance

Calculation

Given, Z = 3 + j4

\(Y={1\over 3+j4}\times {3-j4\over 3-j4}\)

\(Y={3-j4\over (3)^2\space +(4)^2}\)

\(Y={3-j4\over 25}\)

Y = 0.12 − j0.16

Concept:

Impedance (Z) = \({1\over Admittance (Y)}\)

Z = R + jX

where, R = Resistance & X = Reactance

Y = G + jB

where, G = Conductance & B = Susceptance

Calculation:

Given, Y = 3 + j4

\(Z={1\over 3+j4}\)

\(Z={1\over 3+j4}\times{3-j4\over 3-j4}\)

\(Z={1\over 25}(3-j4)\)

Resistance, R = \(\frac{3}{25}\Omega\)