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PHY301 – Circuit Theory
Virtual University
PHY 301
LECTURE 21
Example:
Solution:
Calculate the voltage V
o.
we want to calculate the voltage V
0.
The circuit can be redrawn as
V can be given as
0
V = 2k(I +I )
0
1 2
Now
I = 2V /1k
1
0
= 2(2k(I +I ))/1k
1 2
= 4(I +I )
1 2
I = 4I +4I2
1
1
-3I = 4I
1
2
I = -4/3 I
1
2
Now KVL for loop 2
4kI +4k(I +I ) +2k(I +I ) =6
2
1 2
1 2
4kI +4kI +4kI +2kI +2kI = 6
2
1
2
1
2
10kI +6kI =6
2
1
5kI +3kI =3
2
1
We know
I =-4/3 I
1
2
So
5kI +3k(-4/3)I = 3
2
2
5kI - 4kI =3
2
2
I = 3mA
2
So
I = (-4/3) I
1
2
I =-4mA
1
Now
V = 2k(I +I )
0
1 2
= 2k(-4m + 3m)
V =-2 volts
0
Virtual University of Pakistan
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PHY301 – Circuit Theory
Example:
Solution:
Calculate the voltage V
o.
We want to find the voltage V The circuit can be redrawn as
0.
Here
I = -4mA
2
I =-1mA
3
Now
Vx = -(I +I )1k
3 4
and
I = 2Vx/1k
1
I = -2(I +I )
1
3 4
= 2 - 2I
4
Now KVL for loop4
-1k(I +I ) +1k(I +I ) +1k(I +I –I ) +1k(I - I ) +2kI = 0
4 3
4 3
4 3 2
4 1
4
2kI – 2 -1kI +1 +4 +2kI +1k(I -2 +2I )= 0
4
4
4
4
4
6kI +1 = 0
4
6kI = -1
4
I =-1/6k
4
Now
V = 1k(I + I )
0
4
3
= 1k( -1/6 – 1)
= 1k(-.166 -1)
V = -1.166 volts
0
Example:
Find loop currents.
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PHY301 – Circuit Theory
Solution:
currents.
We use the coupling equation technique to find loop currents to find
the loop
The KVL equation for this supermesh
-7 +1(I –I ) +3(I –I ) +1I =0
1 2
3 2
3
I -4I +4I =7
1 2
3
(1)
And for mesh2
1(I –I )) +2I +3(I – I ) =0
2 1
2
2 3
-I +6I -3I =0
1
2 3
(2)
Coupling equation
I –I = 7
1 3
(3)
solving (1) and (2)
6I -24I +24I = 42
1
2
3
-4I +24I -12I = 0
1
2
3
2I
1
+12I = 42
3
(4)
Subtracting (3) and (4)
2I +12I = 42
1
3
2I - 2I = 14
1
3
14I = 28
3
I =2 A
3
putting this in (1)
I -2 =7
1
I =9A
1
and hence I can be calculated by putting I and I in (1) or (2)
2
1
2
from 1
9 – 4I +8 =7
2
-4I = -17 -7
2
4I =10
2
I =2.5A
2
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