determine the current I1
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Explanation:
According to kirchhoff's first rule to O
−l
1
−l
2
−l
3
=0 or
l
1
+l
2
+l
3
=0 ...(i)
If V
0
is the electric potential at O
V
1
,V
2
and V
3
be the potential at A,B and C respectively then V
0
−V
1
=l
1
R
1
.
V
0
−V
2
=l
2
R
2
and V
0
−V
3
=l
3
R
3
This, l
1
=(
R
1
V
0
−V
1
),l
2
=(
R
2
V
0
−V
2
), and l
3
=(
R
3
V
0
−V
3
)
putting volume of l
1
,l
2
and l
3
in (I) we get
R
1
V
0
−V
1
+
R
2
V
0
−V
2
+
R
3
V
0
−V
3
=0
or V
0
[
R
1
1
+
R
2
1
+
R
3
1
]−[
R
3
R
1
V
1
+
R
2
V
2
+V
3
]=0
or V
0
=[
R
3
R
1
V
1
+
R
2
V
2
+V
3
][
R
1
1
+
R
2
1
+
R
3
1
]
−1
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