Question

In a metre bridge experiment, the null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y?

Options

• 50 cm

• 80 cm

• 40 cm

• 70 cm

Answer 1

50 cm

Explanation:

From the balance condition for the metre bridge experiment, we have

`"R"_1/"R"_2 = "l"_1/"l"_2`

`"R"_1/"R"_2 = "l"_1/((100 - "l"_1))` ...............(i)

In 1^st case, we have, 

R₁ = X; R₂ = Y; l₁ = 20 cm,

l₂ = 100 - 20 = 80 cm

Therefore, equation (i) becomes

`"X"/"Y" = 20/80 = 1/4` ..............(ii)

Similarly, in the 2^nd case,

R₁ = 4X, R₂ = Y and l₁ = l ⇒ l₂ = 100 - l

Therefore, equation (i) becomes

`(4"X")/"Y" = l/(100 - l)` .............(iii)

Using (ii),

`4(1/4) = l/(100 - l)`

∴ 100 - l = l or 2l = 100

∴ l = 50 cm