Question

Two wires A and B of equal lengths are connected in left and right gap of a meter bridge, null point is obtained at 40 cm from left end. Diameters of the wire A and B are in that ratio 3 : 1. The ratio of specific resistance of A to the of B is ____________.

विकल्प

• 4 : 1

• 3 : 1

• 6 : 1

• 8 : 1

Answer 1

Two wires A and B of equal lengths are connected in left and right gap of a meter bridge, null point is obtained at 40 cm from left end. Diameters of the wire A and B are in that ratio 3 : 1. The ratio of specific resistance of A to the of B is 6 : 1.

Explanation:

The specific resistance of a wire of diameter d is

ρ = `"R" "A"/"l" = ("R"π"d"^2)/(4"l")`

`ρ ∝ "Rd"^2` .....(∵ l is constant)

At null point in a meter bridge, `"R"_"A"/"R"_"B" = 40/((100 - 40)) = 2/3`

Given, d_A : d_B = 3 : 1

∴ `(ρ_"A")/(ρ_"B") = ("R"_"A""d"_"A"^2)/("R"_"B""d"_"B"^2) = 2/3 xx (3/1)^2 = 6/1` or 6 : 1