Which is true for admittance?

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Examoogle · Accepted Answer

$Y = \frac{1}{Z}$

Explanation: Admittance is defined as the reciprocal of impedance in an A.C. circuit. It represents the ease with which current flows through an electrical circuit.

Working Principle: In an A.C. circuit, impedance ($Z$) is the complex opposition to current flow consisting of resistance ($R$) and reactance ($X$). Admittance ($Y$) is the complex ratio of current to voltage ($Y = I/V$), which mathematically equates to $Y = 1/Z$. It is measured in Siemens ($S$) and consists of Conductance ($G$) and Susceptance ($B$).

Key Formulas: $Y = \frac{1}{Z}$ — Fundamental definition of admittance as reciprocal of impedance; $Y = G + jB$ — Complex form of admittance where $G$ is conductance and $B$ is susceptance

Key Points: Admittance is the complex reciprocal of impedance.; The SI unit of admittance is Siemens (S), previously known as Mho.; Higher admittance signifies a lower impedance, allowing more current for a given voltage.; For a purely resistive circuit, admittance is simply the reciprocal of resistance (Conductance).

Advantages: Simplifies calculations in parallel A.C. circuits.; Directly additive when elements are in parallel, similar to conductances in D.C. circuits.

Disadvantages: Requires complex number arithmetic to compute from series components.; Does not provide direct information about individual components like $R, L, C$ without decomposition.

Applications: Analysis of parallel RLC networks.; Power system network modeling and load flow analysis.

Additional Info: Admittance is often represented in polar form as $Y = |Y|\angle-	heta$, where $	heta$ is the phase angle of impedance.. Option A is incorrect as $Y 
eq X$ (Reactance). Option B is incorrect as $Y$ is the inverse of $Z$. Option C is incorrect as $X$ typically denotes reactance.

Answer: D is correct — Admittance ($Y$) is mathematically defined as the reciprocal of impedance ($Z$), expressed as $Y = \frac{1}{Z}$.

Exam Tip: When analyzing parallel circuits, always convert individual branch impedances to admittances ($Y_n = 1/Z_n$) to sum them easily: $Y_{total} = Y_1 + Y_2 + ... + Y_n$.

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