Which is true for admittance?

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Examoogle · Accepted Answer

Y=√G²+B²

Explanation: Admittance ($Y$) is defined as the reciprocal of impedance ($Z$) in an AC circuit. It represents the ease with which current flows through the circuit, expressed in Siemens ($S$), and is composed of conductance ($G$) and susceptance ($B$) in a complex rectangular form, $Y = G - jB$. Working Principle: In a parallel AC circuit, the total admittance is the complex sum of the conductances and susceptances of the individual branches. Conductance $G$ is the real part representing energy dissipation, and susceptance $B$ is the imaginary part representing energy storage in reactive components. The magnitude of the admittance is calculated using the Pythagorean theorem based on the orthogonal nature of the real and imaginary axes, resulting in $Y = \sqrt{G^2 + B^2}$. Key Formulas: $Y = \frac{1}{Z}$ — Admittance is the reciprocal of Impedance; $Y = G + jB$ — Complex form of Admittance; $|Y| = \sqrt{G^2 + B^2}$ — Magnitude of Admittance Key Points: Admittance is measured in Siemens ($S$) or Mho ($\Omega^{-1}$).; Conductance ($G$) is the real part of admittance, while susceptance ($B$) is the imaginary part.; Admittance provides a simpler approach to analyzing parallel circuits compared to impedance. Advantages: Simplifies calculations for parallel circuit branches.; Easily additive for parallel connections. Disadvantages: Less intuitive than impedance for series circuit analysis.; Can be confusing due to the negative sign in inductive susceptance. Applications: Power system network analysis (Y-bus matrix).; Parallel resonance circuits.; AC motor control and power factor correction. Additional Info: The susceptance $B$ is positive for capacitors ($B_C = \omega C$) and negative for inductors ($B_L = -\frac{1}{\omega L}$).. Option A, B, and D are mathematically incorrect representations of the relationship between admittance and its components. Answer: C is correct — The magnitude of admittance is calculated by the square root of the sum of the squares of conductance and susceptance, $Y = \sqrt{G^2 + B^2}$. Exam Tip: Remember that while impedance ($Z$) sums easily in series, admittance ($Y$) sums easily in parallel. Always convert to polar form for multiplication/division and rectangular for addition/subtraction.

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