Admittance Method

Admittance method is used for solving parallel AC circuits. The admittance shows the reliability of the electrical circuit to allow the electric current to pass through it. First of all, we must know the meanings of some terms used in the Admittance Method.

Admittance

The reciprocal of the impedance of an AC circuit is known as Admittance of the circuit. Since impedance is the total opposition offered to the flow of alternating current in an AC circuit. Therefore, Admittance is defined as the effective ability of the circuit due to which it allows the alternating current to flow through it. It is represented by (Y). The old unit of admittance is mho (Ʊ).Its new unit is Siemens. The circuit having an impedance of one ohm has an admittance of one Siemens. The old unit was mho.

admittance-eq1

Contents:

Application of Admittance Method

Consider the 3-branched circuit shown in the figure below. Total conductance is found by merely adding the conductance of three branches. Similarly, total susceptance is found by algebraically adding the individual susceptance of different branches.

application-of-admittanceTotal conductance G = g1 + g2 + g3 +…..
Total susceptance B = (-b1) + (-b2) + b3….
Total admittance Y = ( G2 + B2)
Total current I = VY ; Power Factor cosΦ = G / Y

Steps for Solving Circuit by Admittance Method

Consider a parallel AC circuit having resistance and capacitance connected in series and resistance and inductance also connected in series as shown in the figure below.

admittance-method-figureStep 1 – Draw the circuit as per the given problem.

Step 2 – Find impedance and phase angle of each branch.

admittance-eq2

Step 3 – Now, find Conductance, Susceptance and Admittance of each branch.

admittance-eq3

Step 4 – Find the algebraic sum of conductance and susceptance.

admittance-eq4

Step 5 – Find the total Admittance (Y) of the circuit.

admittance-eq5

Step 6 – Find the various branch currents of the circuit.

admittance-eq6

Step 7 – Now, find the total current I of the circuit.

admittance-eq7

Step 8 – Find the phase angle of the whole circuit.

admittance-eq8

Phase angle will be lagging if B is negative.

Step 9 – Now, find the power factor of the circuit.

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Admittance Triangle

Admittance triangle is also represented similarly to impedance triangle. As the impedance (Z) of the circuit has two rectangular components, resistance (R) and reactance (X). Similarly, the admittance (Y) also has two components, conductance (g) and susceptance (b). The Admittance triangle is shown below.

Admittance-triangle-phasor-diagram

Conductance

The base of the Admittance triangle is known as Conductance, shown in the figure above.

admittance-eq10The value of conductance is always positive irrespective of the circuit parameters.

Susceptance

The perpendicular of the Admittance triangle is called Susceptance.

admittance-eq11Susceptance is positive for capacitive reactance as shown in the above figure (A) and is negative for inductive reactance as shown in figure (B).

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