Question

In a metre bridge experiment, resistance box (with R = 2Ω ) is connected in the left gap and the unknown resistance S in the right gap. If balancing length be 40 cm, calculate value of S​

Answer 1

Case 1 :

Null point is found at l

1

=40 cm

Using balanced Wheatstone bridge condition,

X

2

=

100−l

1

l

1

∴

X

2

=

100−40

40

⟹ X=3Ω

Case 2 :

New null point is found at l

2

=50 cm

Using balanced Wheatstone bridge condition,

X

′

2

=

100−l

2

l

2

∴

X

′

2

=

100−50

50

⟹ X

′

=2Ω

Since the unknown resistance gets decreased, thus we have to connect a resistance R in parallel to X so that X

′

comes out to be 2Ω.

Thus resistance of parallel combination X

′

=

X+R

XR

∴ 2=

3+R

3R

⟹ R=6Ω

Hence 6Ω must be connected in parallel to unknown resistance X.