ac parallel circuits there are 3 methods to solve the a.c parallel circuits - method of vectors...

AC Parallel circuits• There are 3 methods to solve the a.c parallel circuits- Method of vectors -Symbolic method or ‘j’ method-Admittance or ‘Y’ method

a)Method of Vectors• Consider the a.c parallel circuit to which a voltage ‘E’ Is applied

• I is total current & I1, I2 & I3 branch currents

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Contd..• I1, I2 & I3 are found both in magnitude & direction

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Contd..

• The magnitude of resultant current is given by

• The phase angle of resultant current is given by

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Contd..

• The operator ‘j’• It is similar to operator ‘i’ used in mathematics• Its value is √-1• When a vector multiplied by ‘j’ , it gets rotated by 900 in anticlockwise direction

• P is a vector along X-axis, when it is multiplied by ‘j 2’ it gets rotated by 1800

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Contd..

• Symbolic or ‘j’ method

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Contd..

Admittance ‘Y’ :• It is reciprocal of impedance, Unit is mho • In S.I unit the admittance is Siemen (S)

• If Z1 , Z2 & Z3 are 3 impedances connected in parallel, Total impedance is

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Contd..• Let

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Admittance MethodThe susceptances of the three branches

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Contd..

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• ii) ‘j’ method :

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• iii) Admittance method:

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