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In admittance method, power factor is given by
cosтИЕ=B/G
cosтИЕ=G/Y
cosтИЕ=G/B
cosтИЕ=Y/G
cosтИЕ=G/Y
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╧Х is defined as the ratio of conductance to admittance.
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╧Х is defined as the ratio of conductance to admittance.
Y=G2+B2тАЛ тАФ Relationship between admittance, conductance, and susceptance
cos╧Х=YGтАЛ тАФ Definition of power factor in terms of admittance parameters
The total admittance of a parallel circuit is Y=G+jB. The power factor angle ╧Х is the phase difference between voltage and current. In the admittance triangle, G=Ycos╧Х and B=Ysin╧Х. Thus, dividing the conductance by the admittance yields the cosine of the phase angle, which is the power factor.
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╧Х=1.
Simplifies analysis of complex parallel RLC circuits.
Allows direct calculation of total circuit current using I=V├ЧY.
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).
Power system load flow analysis.
Design of parallel resonant circuits and compensation networks.
Option A (B/G) is the tangent of the phase angle (tan╧Х).
Option C (G/B) is the cotangent of the phase angle (cot╧Х).
Option D (Y/G) is the secant of the phase angle (sec╧Х).
B is correct тАФ 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).
Remember: In impedance (Z) based analysis, cos╧Х=R/Z. In admittance (Y) based analysis, cos╧Х=G/Y. Always match the parameters to the specific triangle (R-X-Z vs G-B-Y).