ELE101/102 Dept of E&E,MIT Manipal 1

Parallel Circuit

Let Z1 & Z2 are the complex impedances

connected in parallel

Z 1Z 2V

I

I 1 I 2

ferencetVtv m Re)1(sin)(

phasorvoltage0VV

21

22

11

III

Z

VI

Z

VI

I1

I2

I

VΦ

ELE101/102 Dept of E&E,MIT Manipal 2

R, L, and C in Parallel

Phasor Diagram -

tVtv m sin)( i(t)

v(t)

R L

Ri CiLi

C 0VV

RI

V

I

Reference

cL II

LI

CI

CLR IIII

90X

VI

;90X

VI;0

R

VI

CC

LLR

ELE101/102 Dept of E&E,MIT Manipal 3

Parallel Circuits

Where G = Conductance B = Susceptance

But,

jBG

AdmittanceZ

1Y

XB

RG

1

1

For any parallel circuit,

ELE101/102 Dept of E&E,MIT Manipal 4

Parallel Circuits

For any parallel circuit,

eqN

NN

eqeqeq

Neq

NN

VYIIII

VYIVYIVYI

jBGZ

YYYY

ZY

ZY

ZY

.....

;....;

1......

1;......

1;

1

21

2211

21

22

11

ELE101/102 Dept of E&E,MIT Manipal 5

Illustration

Two circuits ZA = 5+j2 and ZB = 6 – j8 are in parallel

across a 200V, 50 Hz supply. Find current in each branch,

total current, power factor and power consumed.

ZA = 5+j2

ZB = 6-j8

200V, 50Hz

I

IA

IB

Ans: AI A8.2114.37 BI A13.5320 A72.254.46I cos = 0.9988 lead

Power = 9.297W