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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
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
∠=
−∠=∠=
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,
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
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
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

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L21 1 ph-ac

  • 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