Circuit diagram of metre bridge is shown in figure. The null point is found at a distance of 40 cm from A. If now a resistance of 12 ohmis connected in parallel with S, the null point shifts to 64 cm. Determine the values of R and S.
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When 12Ω resistance is not connected in parallel to S than we can write,
R=S
100−l
1
l
1
l
1
=40cm
∴R=S(
60
40
)=
3
2
S __(I)
Now when 12Ω is connected in parallel to S, then
The effective resistance can be written as
S
1
1
=
S
1
+
12
1
=
12S
12+5
⇒S
1
=
(12+5)
12S
Now we can write
R=S
100−l
′
l
′
⇒l
′
=50cm
i.e. R=
(12+5)
12S
×
50
50
=
12+5
12S
__(II)
Using eq (II) and (I)
3
2
S=
12+5
12S
⇒(12+5)2=36
⇒24+25=36⇒25=12⇒S=6Ω
and R=
3
2
×6=4Ω
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