# 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.**

AC Parallel Circuit:

AC Parallel Circuit:

**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•(cosÎ¸+j•SinÎ¸), {Trigonometric Notation} = Z∠Î¸, {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 = 1/2

*Ï€∗√(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.

#### Reference:

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

#### Author:

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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