134
CHAPTER 18
18.58
Consider a battery of emf
ε
connected between
points
a
and
b
as shown. Applying Kirchhoff’s
loop rule to loop
gives
acbea
( ) ( )
()
11
3
1.0
0
I
1.0
II
−− −
+
13
2
=
or
−=
adbea
(
(1)
Applying the loop rule to loop
gives
) ( )
22
3
3.0
0
I
5.0
−− +
+
23
85
=
or
+
adca
(
=
(2)
For loop
, the loop rule yields
) ( ) ( )
231
3.0
1.0
0
−++
1.0
I
=
or
3
II I
2
+
=
(3)
Solving equations (1), (2) and (3) simultaneously gives
12
4
,
,
27
3
1
27
13
and
27
I
εε
=
−
==
Then, applying Kirchhoff’s junction rule at junction
a
gives
4
17
27
27
13
27
=+
+
=
=
. Therefore,
27
17
27
17
I
ab
R
=
Ω
±²³´
µ²³´
±
±
²
³
´
µ
¶
¶²³´
²
±
¶
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 Fall '10
 STAFF
 Physics, Current, Resistor, Prime number, Electrical resistance, Series and parallel circuits, load resistor

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