AC Parallel Circuit - Current Calculation Method and Resonance

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.


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