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Which is method of solving ac parallel circuit?
Vector method
Admittance method
Complex algebra method
All of above
All of above
Quick Summary: AC parallel circuits can be analyzed using multiple methodologies depending on the complexity of the network. These include graphical representation (Vector), impedance-based reciprocal analysis (Admittance), and complex frequency-domain modeling (Complex Algebra).
AC parallel circuits can be analyzed using multiple methodologies depending on the complexity of the network. These include graphical representation (Vector), impedance-based reciprocal analysis (Admittance), and complex frequency-domain modeling (Complex Algebra).
Y=G+jB — Admittance as sum of Conductance and Susceptance
Itotal=I1+I2+I3 — Kirchhoff's Current Law in phasor form
In a parallel AC circuit, the voltage across all branches is common. The admittance method simplifies the calculation by summing individual branch admittances (Y=G+jB), where Y=Z1. Complex algebra uses the rectangular (a+jb) or polar (r∠θ) form to perform vector arithmetic on impedances and currents.
In parallel circuits, voltage is the reference phasor.
Admittance (Y) is the reciprocal of impedance (Z).
Complex algebra allows addition of complex currents representing magnitude and phase shift.
Vector method (Phasor diagram) provides a visual verification of current phase relationships.
Admittance method simplifies parallel branch arithmetic
Complex algebra handles phase angle summation efficiently
Phasor diagrams provide intuitive understanding of power factor
Vector method becomes tedious for circuits with more than 3 branches
Complex algebra requires proficiency in handling imaginary 'j' operator
Power distribution network analysis
AC motor winding calculations
Resonance frequency tuning circuits
Option A (Vector method) uses geometric summation of phasors.
Option B (Admittance method) is the most efficient algebraic way to handle parallel branches.
Option C (Complex algebra) is the mathematical foundation for both Admittance and Vector methods.
D is correct — All listed methods provide valid mathematical or graphical frameworks for solving AC parallel networks.
Always convert series impedances to admittances (Y=1/Z) before summing parallel branches to save calculation time in competitive exams.