Admittance is a reciprocal of:

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.