Page 326 - Basic Electrical Engineering

Note that when X = X , the component of I in phase with V is I only
C
L
because I cos ϕ = I (as cos ϕ = 1).

3.2.7 AC Parallel Circuits

Parallel circuits are formed by two or more series circuits connected to a
common source of supply. The parallel brances may include a single element

or a combination of elements in series.
Methods for solving ac parallel circuits:

The following three methods are available for solving ac parallel circuits:

1. phasor or vector method
2. admittance method
3. using vector algebra (symbolic method or j-operator method)

These methods are explained with examples as follows.

1. Phasor or vector method

A parallel circuit consisting of three branches has been shown in Fig. 3.29.
Branch 1 consists of R , L , and C in series. Branch 2 is resistive and
1
1
1
capacitive and branch 3 is resistive and inductive. Let the current be I , I ,
2
1
and I in the branch 1, 2, and 3, respectively. The total current drawn by the
3
circuit is the phasor sum of I , I , and I .
2
1
3
Branch 1

Impedance of branch 1,

Current I = V/Z 1
1