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8/6/2019 ET115-2
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1
M.Shakeel
1 380 0 IR IR− − =
xt StampShakeel
8/6/2019 ET115-2
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2
Q1:In the circuit shown find current in each Resistor.
1
1
2
2
1 2
1.895 10 Reisitor
0.33(1.895) 1
1.625 8 Reisitor
4 Reisitor=
1.895 1.625
0.27
I A current in
puting the value of I ineq
I
I A current in
Current in I I
A
= = Ω
= +
= = Ω
Ω −
= −
=
1 1 2
1 1 2
1 2
2 2 1
2 2 1
2 1
2 1
12
12
2 1
2
1 1
1
1 0 4 ( ) 2 0 0
1 0 4 4 2 0
1 4 4 2 0 1
2
8 4 ( ) 1 2 0
8 4 4 1 2
1 2 4 1 2 2
1 2 4 1 2
4 1 2
1 2
4 1 2
1 2 1 2
0 .3 3 1 3
1
1 4 4 ( 0 .3 3
s t
n d
L o o p
I I I
I I I
I I e q
L o o p
I I I
I I I
I I e q
I I
I I
I I
I I e q
p u t in g t h e v a l u e o f I i n e q
I I
+ − − =
+ − =
− = ⎯ ⎯→
+ − − =
+ − =
− = ⎯ ⎯→
= +
+=
= +
= + ⎯ ⎯→
−
1 1
1
1
1) 2 0
1 4 1 .3 3 4 2 0
1 2 .6 7 2 0 4
2 4
1 2 . 6 7
I I
I
I
+ =
− − =
= +
=
xt StampShakeel
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3
Q2: Two batteries, A and B, are connected to the circuit shown.Battery A, 50cells, Battery B, 40 cells E.M.F. 2 volts/cell. InternalResistance. 0.01 ohm/cell. Find the current flowing in each batteryand in 0.8ohm resistor.
1 2
1 2
1 2
2 1
Battry A,EMF=50× 2=100V
Battry A,Resistance=50× 0.01=0.5Ω
Battry B,EMF= 40×2=80V
Batt ry B,Resistance 40 0 .01 0 .4
1
0.5 (0.4 0 .2) 80 100 0
0.5 0.6 20 0
0.5 0.6 202
0.8( ) (0.2 0.4)
st
nd
Loop
I I
I I
I I eq Loop
I I I
= × = Ω
− + + − =
− − =
− = ⎯ ⎯→
+ + +2
2 1 2
1 2
2 1
12
12
2 1
2
1 1
1 1
1
80 0
0.8 0.8 0.6 80 0
0.8 1.4 80
1.4 80 0.8
80 0.8
1.4
0.880
1.4 1.457.14 0 .57
0.5 0.6(57.14 0.57 ) 20
0.5 34.28 0.342 20
0.842 20 34.2
I I I
I I eq
I I
I I
I I
I I eq
puting the value of I in eq
I I
I I
I
− =
+ + − =
+ = ⎯ ⎯→
= −
−=
= −
= − ⎯ ⎯→
− − =
− + =
= + 8
1
1
1
2
2
1 2
54.28
0.842
64.46
57.14 0.57(64.46)
20.39
0.8 Reisitor=64.46 20.39
84.75
I
I A current in Battery A
puting the value of I in eq
I
I A current in Battry B
Current in I I
A
=
= =
= −
= =
Ω +
= +
=
xt StampShakeel
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4
Q3: In the circuit shown find magnitude and direction of current ineach resistor. Internal resistance of cells negligible.
( )
1 1 2
1 1 2
1 2
2 2 1
2 2 1
2 1
2 1
12
12
2 1
2
1
1
4 10( ) 4 0
4 10 10 4
14 10 4 1
2
5 10( ) 2 0
5 10 10 2
15 10 2 2
15 10 2
10 2
15
10 2
15 15
0.667 0.133 3
1
14 10(
st
nd
Loop
I I I
I I I
I I eq
Loop
I I I
I I I
I I eq
I I
I I
I I
I I eq
puting thevalueof I ineq
I
+ − − =
+ − =
− = ⎯⎯→
+ − − =
+ − =
− = ⎯⎯→
= +
+=
= +
= + ⎯⎯→
−10.667 0.133) 4 I + =
1 1
1
1
1
1
2
2
1 2
14 6.67 1.33 4
7.33 1.33 45.33
7.33
0.727 4 Reisitor
3
0.667(0.727) 0.133
0.618 5 Reisitor 10 Reisitor=
0.727 0.618
0.109
I I
I
I
I A current in
puting thevalueof I ineq
I
I A current inCurrent in I I
A
− − =
= +
=
= = Ω
= +
= = Ω
Ω −
= −
=
xt StampShakeel
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5
Q4:Two batteries A and B are connected to the circuit as shown,Battery A 25 cells, Battery B, 20 cells ,EMF per cell 2 volt, the internalresistance 0.01ohm/cell.Find the current flowing in each battery andin 5ohm resistor.
1 2
1 2
1 2
2 1 2
BattryA,EMF=25×2=50V
BattryA,Resistance=25×0.01=0.25Ω
BattryB,EMF=20×2=40V
BattryB,Resistance 20 0.01 0.2
1
0.25 (0.2 2) 40 50 0
0.25 2.2 10 0
0.25 2.2 10 1
2
5( ) (2 0.2) 40
st
nd
Loop
I I
I I
I I eq
Loop
I I I
= × = Ω
− + + − =
− − =
− = ⎯⎯→
+ + + −
2 1 2
1 2
2 1
12
12
2 1
0
5 5 2.2 40 0
5 7.2 40 2
7.2 40 5
40 5
7.2
540
7.2 7.2
5.55 0.694 3
I I I
I I eq
I I
I I
I I
I I eq
=
+ + − =
+ = ⎯⎯→
= −
−=
= −
= − ⎯⎯→
2
1 1
1 1
1
1
1
1
2
2
1
0.25 2.2(5.55 0.694 ) 10
0.25 12.21 1.53 10
1.78 10 12.21
22.21
1.78
12.48
35.55 0.694(12.48)
3.11
puting the value of I in eq
I I
I I
I
I
I A current in Battery A
puting the value of I in eq I
I A current in Battry B
Curre
− − =
− + =
= +
=
= =
= −
= − =
1 25 Reisitor=
12.48 ( 3.11)
9.37
nt in I I
A
Ω +
= + −
=
xt StampShakeel
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6
Q5: in the circuit shown find current in each branch and the current inBattery, What is the difference of potential between X and Y.
1 1 2
1 1 2
1 2
2 1 2
2 1 2
1 2
1 2
1 2
1
2 2
2 2
2
1
2
3
1
1
(1 3) 2( ) 4 0
4 2 2 46 2 4
2
(4 5) 2( ) 4 0
9 2 2 4
2 11 4
2 4 11
2 5.5
6(2 5.5 ) 2 4
12 33 2 4
12 31 41
st
nd
Loop
I I I
I I I I I eq
Loop
I I I
I I I
I I eq
I I
I I eq
puttingthevalueof I ineq
I I
I I
I
⎯⎯→
⎯⎯→
⎯⎯→
+ + + − =
+ + =
+ =
+ + + − =
+ + =
+ =
= −
= −
− + =
− + =
− =
22 4 31 I − =
2
2
2
2
1
1
1 2
3
8 31
831
0.258
2 5.5(0.258)
0.581
sup
0.581 0.258
0.839 potentialdifference between and
xy Ax
I
I
I Acurrentinbranch AXB
putting thevalueof I ineq
I
I Acurrentinbranch AYB
current plyed frombattry I I
A x y
V V V
=
=
=
= −
=
= +
= +
=
= −
1
2
0.581 1 0.581
0.258 4 1.032
0.581 1.032
0.451
Ay
Ax AX
Ay AY
xy
xy
V I R
V I R V
V
V V
= × ⇒ × =
= × ⇒ × =
= −
= −
xt StampShakeel
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7
Q6: In the circuit shown find magnitude and direction of current ineach resistor. Internal resistance of cells negligible.
1 1 2
1 1 2
1 2
2 1 2
2 1 2
2 1
2 1
2 1
12
2 1
2
1
1
4 10( ) 4 0
4 10 10 4 014 10 4 1
2
10( ) 5 2 0
10 10 5 2 0
15 10 2
15 10 2 2
15 2 102 10
15
0.1333 0.6667 3
1
14
st
nd
Loop
I I I
I I I I I eq
Loop
I I I
I I I
I I
I I eq
I I
I I
I I eq
putting the value of I in eq
I
+ + − =
+ + − =
+ = →
− + − + =
− − − + =
− − = −
+ = →
= −
−=
= − →
+ 1
1 1
1
1
1
10(0.1333 0.6667 ) 4
14 1.333 6.667 4
7.333 5.335.333
7.333
0.727 , 4
I
I I
I
I
I A Current in resistor
− =
+ − =
=
=
= Ω
1
2
2
1 2
3
0.1333 0.6667(0.727)
0.3515 , 5
10
0.727 0.3515
0.3755
puttingthevalueof I ineq
I
I A Current in resistor
Currentin resistor I I
A
= −
= − Ω
Ω = +
= −
=
xt StampShakeel
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8
Q1:What are the current in the circuit in fig.
Use voltage source 1
1
1 1 1
2.7 1.8
1
0.9259
11.08
0.9259
1.2 1.08
2.28
T
T
R
R
R K
R R R
R K
= +
=
= ⇒ Ω
= +
= +
= Ω
xt StampShakeel
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9
'1
' 32
3 2
'
2
'
2
' '
3 2
'
3
1 04.386
2.28
4 .386
2 .74 .386
2 .7 1 .8
2 .632
4 .3 86 2 .632 1 .75 4
T
T
T
T
T
V I
R
I m
I m A
R I I
R R
I
I m A
I I I
A
I m A
=
= ⇒
=
= ×+
= ×+
=
= −
= − =
Use voltage source 2
2
1 1 1
1.2 2.7
1 1.203
0.83
0 .8 3 1 .8
2.63
20
2.63
T
T
T
T
T
T
R
R
R K
R R R
R
R K
V I
R
I
= +
=
= Ω
= +
= +
= Ω
=
=
xt StampShakeel
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10
''
2
'' 3
1
3 1
''
1
''
1
'' ''
3 1
''
3
''
3
' ''
1 1 1
1
1
' ''
2 2 2
2
2
' ''
3 3 3
3
3
7 .6
7 .6
2 .77 .6
2 .7 1 .2
5 .263
7 .6 5 .263
2 .337
4 .386 5 .263
9 .649
2 .632 7 .6
10 .23
2 .337 1 .754
0 .
T
T
T
I m A
I m A
R I I
R R
I
I m A
I I I
I
I m A
I I I
I
I m A
I I I
I
I m A
I I I
I
I
=
=
= ×+
= ×+
=
= −
= −
=
= +
= +
=
= +
= +
=
= −
= −
= 583m A
xt StampShakeel
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11
Q2: Find current in R2 of figure, by using the superpositiontheorem.
Using Vs1
2 3
1 1 1 R R R
= +
2
' 32
3 2
'
2
'
2
1 1 1
100 100
10.02
50
50 100150
10
150
0.0667
1000.0667
100 100
0.0333
T
T
T
T
T
T
T
T
R
R
R
R R R
R R
V I
R
I
I A
R I I
R R
I
I A
= +
=
= Ω
= +
= +
= Ω
=
=
=
= ×
+
= ×+
=
Using Vs2
1 2
3
'' 12
1 2
''2
''
2
1 1 1
1 1 1
1 0 0 1 0 0
10 . 0 2
5 0
5 0 1 0 0
1 5 0
5
1 5 0
0 . 0 3 3 3
1 0 00 . 0 3 3 3 1 0 0 1 0 0
0 . 0 1 6 6 6 7
T
T
T
T
T
T
T
T
R R R
R
R
R
R R R
R
R
V I
R
I
I A
R I I
R R
I
I A
= +
= +
=
= Ω
= +
= +
= Ω
=
=
=
= ×+
= ×+
=
' ''
2 2 2
2
2
0 .0333 0 .01667
0.05
I I I
I
I A
= +
= +
=
xt StampShakeel
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12
Q3: Calculate the current in each branch of network shown.
Using Vs1
2 3
1
'
1
' 3
2
3 2
'
2
'
2
' '
3 2
'
3
'
3
1 1 1
1 1 1
3 10
10.433
2.31
2 .31 2
4.31
6
4.31
1.39
1.39
101.39
10 3
1.071
1 .39 1 .071
0.321
T
T
T
T
T
T
T
T
T
R R R
R
R
R
R R R
R
R
V I
R
I
I A
I A
R I I
R R
I
I A
I I I
I
I A
= +
= +
=
= Ω
= +
= +
= Ω
=
=
=
=
= ×+
= ×+
=
= −
= −
=
xt StampShakeel
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13
Using Vs2
1 3
3
' ''
1 1 1
1
1
'' ' ''
2 2 2 2
'' 31 2
3 1
''
1 2
''
1
1 1 1
1 1 1
2 10
10.6
1.667
1.667 3
4.667
41.39 0.714
4.667
0.857 0.676
0.857
1.071 0.857
100.857 0.214
10 2
0.
T
T
T
T
T
T
T
T
R R R
R
R
R
R R R
R
R
V I I I I
R
I I
I A I A
I A I I I
R I I I
R R
I I A
I
= +
= +
=
= Ω
= +
= +
= Ω
= = −
= = −
= =
= = −
= × = −+
= × =+
=' ''
3 3 3
'' ''
3 1 3
''
3 3
''
3
714
0.321 0.143
0.857 0.714 0.464
0.143
T
A I I I
I I I I
I I A
I A
= +
= − = +
= − =
=
xt StampShakeel
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14
Q1: Find current in 10ohm resistor by using thevenin theorem.
Open 10ohm resistor from AB terminals
1 2
2
6 3
9
182
9
2 6
12
T
T
T
th
th
R R R
R
R
V I A
R
V IR
= +
= +
= Ω
= ⇒ ⇒
= ⇒ ×
=V V
xt StampShakeel
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15
Short circuited Voltage source
1 1 10.5
3 6
2
2 4
6
th
th
R
R
R
R
= + ⇒
= Ω
= +
= Ω
6 10
16
1216
0.75
10 0.75
T
T
R
R
V I R
I A
Current in Resistor A
= +
= Ω
= ⇒
=
Ω =
xt StampShakeel
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16
Q2:Find current in 6 ohm resistor by using Thevenin Theorem.
Open 6ohm resistor
3 4
4 3 1
8
6
8
0.75
( )
0.75(3 1)
3
T
T
T
T
th T
th
th
R
V I
R
I
V I R R
V
= + +
= Ω
= ⇒
= Α
= +
V V
= +
=
Short circuited voltage source
3 1
4
R
R
= +
= Ω
1 1 10.5
4 4T R
= + ⇒
xt StampShakeel
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17
1
0 .5
2
2
T
T
th
R
R
R
=
= Ω
= Ω
6 2
8
3
8
0.375
6 0.375
R
R
V I
R
I
I
C urren t in R esistor
= +
= Ω
=
=
= Α
Ω = Α
xt StampShakeel
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