This document discusses parallel circuits and their analysis. It defines that for components in parallel, the total current is the sum of the individual branch currents. The total impedance of a parallel combination is calculated using the admittance method where the total admittance is the sum of the individual branch admittances. An example problem is given to find the currents, total current, power factor, and power for a parallel RLC circuit connected to a 200V, 50Hz voltage source.

1. ELE101/102 Dept of E&E,MIT Manipal 1
Parallel Circuit
Let Z1 & Z2 are the complex impedances
connected in parallel
Z 1
Z 2V
I
I 1
I 2
ferencetVtv m Re)1(sin)( −−= ω
phasorvoltage0VV −−−−−°∠=
21
2
2
1
1
III
Z
V
I
Z
V
I
+=
== I1
I2
I
VΦ

2. ELE101/102 Dept of E&E,MIT Manipal 2
R, L, and C in Parallel
Phasor Diagram -
tVtv m ω= sin)( i(t)
v(t)
R L
Ri Ci
Li
C°∠= 0VV
RI
V
I
Reference
cL II −
LI
φ
CI
CLR IIII ++=
90
X
V
I
;90
X
V
I;0
R
V
I
C
C
L
LR
∠=
−∠=∠=

3. ELE101/102 Dept of E&E,MIT Manipal 3
Parallel Circuits
Where G = Conductance
B = Susceptance
But,
jBG
Admittance
Z
1
Y
±=
==
X
B
R
G
1
1
≠
≠
For any parallel circuit,

4. ELE101/102 Dept of E&E,MIT Manipal 4
Parallel Circuits
For any parallel circuit,
eqN
NN
eqeq
eq
Neq
N
N
VYIIII
VYIVYIVYI
jBG
Z
YYYY
Z
Y
Z
Y
Z
Y
=+++=
===
±==+++=
===
.....
;....;
1
......
1
;......
1
;
1
21
2211
21
2
2
1
1

5. ELE101/102 Dept of E&E,MIT Manipal 5
Illustration
Two circuits ZA = 5+j2 Ω and ZB = 6 – j8 Ω are in parallel
across a 200V, 50 Hz supply. Find current in each branch,
total current, power factor and power consumed.
ZA = 5+j2 Ω
ZB = 6-j8 Ω
200V, 50Hz
I
IA
IB
Ans: =AI A8.2114.37 °−∠ =BI A13.5320 °∠
A72.254.46I °∠= cosφ = 0.9988 lead
Power = 9.297W

6. ELE101/102 Dept of E&E,MIT Manipal 5
Illustration
Two circuits ZA = 5+j2 Ω and ZB = 6 – j8 Ω are in parallel
across a 200V, 50 Hz supply. Find current in each branch,
total current, power factor and power consumed.
ZA = 5+j2 Ω
ZB = 6-j8 Ω
200V, 50Hz
I
IA
IB
Ans: =AI A8.2114.37 °−∠ =BI A13.5320 °∠
A72.254.46I °∠= cosφ = 0.9988 lead
Power = 9.297W