In admittance method, power factor is given by

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Examoogle · Accepted Answer

cos∅=G/Y

Explanation: In an A.C. circuit represented by the admittance triangle, the admittance $Y$ is the hypotenuse, while the conductance $G$ is the base and the susceptance $B$ is the vertical height. The power factor $cos \phi$ is defined as the ratio of conductance to admittance. Working Principle: The total admittance of a parallel circuit is $Y = G + jB$. The power factor angle $\phi$ is the phase difference between voltage and current. In the admittance triangle, $G = Y \cos \phi$ and $B = Y \sin \phi$. Thus, dividing the conductance by the admittance yields the cosine of the phase angle, which is the power factor. Key Formulas: $Y = \sqrt{G^2 + B^2}$ — Relationship between admittance, conductance, and susceptance; $cos \phi = \frac{G}{Y}$ — Definition of power factor in terms of admittance parameters Key Points: Conductance $G$ represents the real part of admittance and is measured in Siemens ($S$).; Susceptance $B$ represents the imaginary part of admittance, related to inductive or capacitive components.; The power factor is dimensionless and indicates the ratio of active power to apparent power.; In a purely resistive circuit, $B=0$, so $Y=G$ and $cos \phi = 1$. Advantages: Simplifies analysis of complex parallel RLC circuits.; Allows direct calculation of total circuit current using $I = V imes Y$. Disadvantages: Requires conversion from impedance ($Z$) to admittance ($Y$) which can be algebraically tedious for large networks.; Susceptance sign conventions can lead to confusion if not handled with care (inductive vs capacitive). Applications: Power system load flow analysis.; Design of parallel resonant circuits and compensation networks. Additional Info: Option A ($B/G$) is the tangent of the phase angle ($tan \phi$).. Option C ($G/B$) is the cotangent of the phase angle ($cot \phi$).. Option D ($Y/G$) is the secant of the phase angle ($sec \phi$). Answer: B is correct — The power factor of an A.C. circuit is defined by the ratio of the real part of the admittance (conductance $G$) to the magnitude of the admittance ($Y$). Exam Tip: Remember: In impedance ($Z$) based analysis, $cos \phi = R/Z$. In admittance ($Y$) based analysis, $cos \phi = G/Y$. Always match the parameters to the specific triangle (R-X-Z vs G-B-Y).

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