Download BEE-AC-Parallel-circuits

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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..
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• 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..
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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 Method
The susceptances of the three branches
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• ii) ‘j’ method :
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• iii) Admittance method:
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