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