AC Parallel Circuit

AC Parallel Circuit:
The circuit in which number of branches are connected in parallel, such that the voltage across them is same, are called ac-parallel circuit. The total current taken by various branches of parallel circuit as a whole is the phasor sum of the currents in that branches. The total current in such cases can be calculated by either of the three methods: i) Phasor Method, ii) Admittance Method, and iii) Symbolic Method OR j operator method.

i) Phasor Method: This method of finding the resultant current by drawing a phasor diagram gives clear insight into the problem. However drawing the phasor diagram takes a lot of time and drawing errors cannot be eliminated.

ii) Admittance Method: In this method, admittance of the circuit is calculated in which G is reciprocal of the R and is termed as Conductance. While, B is reciprocal of X and is termed as Susceptance.

iii) Symbolic Method: Z = (R + j•X), {Rectangular OR Cartesian Notation} = Z•(cosθ+j•Sinθ), {Trigonometric Notation} = Z∠θ, {Polar Notation}.

Resonance in parallel circuit: Resultant current drawn by a resonant parallel circuit is minimum, and the circuit is normally called Rejector circuit. If in a parallel circuit one branch consists of R and L in series and another branch consists of C then the Resultant frequency, fo = 1/2π∗√(1/LC-R²/L²) Hz. The Phenomenon of Resonance in parallel circuits is normally termed as Current Resonance. Such type of circuit is quite useful in Radio Network.


V N Mittle and Arvind Mittal, "Basic Electrical Engineering," TATA McGRAW Hill, Tenth Reprint, 2009.


Paramjeet Singh Jamwal worked as an Assistant Professor in Electrical and Electronics Engineering Department of Roorkee College of Engineering (RCE), Roorkee, Uttarakhand, India (2017).

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