Question

Two resistances prepared from the wire of the same material having diameters in the ratio 2 : 1 and lengths in the ratio 2 : 1 are connected in the left gap and right gap of Wheatstone's meter bridge respectively. The distance of the null point from the left end of the wire is ______ 

Options

• 66.7 cm

• 33.3 cm

• 25 cm

• 50 cm

Answer 1

Two resistances prepared from the wire of the same material having diameters in the ratio 2 : 1 and lengths in the ratio 2 : 1 are connected in the left gap and right gap of Wheatstone's meter bridge respectively. The distance of the null point from the left end of the wire is 33.3 cm.

Explanation:

`D_1/D_2 = 2/1`

`ℓ_1/ℓ_2 = 2/1`

`R_1 = (rhoℓ_1 4)/(D_1^2)`

`R_2 = (rhoℓ_2 4)/(D_2^2)`

`R_1/R_2 = (rhoℓ_1 4)/D_1^2 xx D_2^2/(rhoℓ_2 4) = ℓ_1/ℓ_2 xx (D_2^2)/(D_1^2)`

= `2 xx 1/4 = 1/2`

`L_1/L_2 = 1/2`

`L_1 + L_2 = 100  cm`

2L₁ = L₂

3L = 100

∴ `L_1 = 100/3 = 33.3  cm`