Question

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 3:2 and 2:3, then the ratio of the current passing through the wire will be ____________.

पर्याय

• 2:3

• 3:2

• 8:27

• 27:8

Answer 1

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 3:2 and 2:3, then the ratio of the current passing through the wire will be 8:27.

Explanation:

`1_1 : 1_2 = 3 : 2`

`"r"_1 : "r"_2 = 2 : 3`

`"I"_1 : "I"_2 = ?`

`"R"_1 = rho 1_1/(pi"r"_1^2)`

`"R"_2 = rho 1_2/(pi"r"_2^2)`

`"R"_1/"R"_2 = 1_1/1_2 (pi"r"_2^2)/(pi"r"_^2)`

`= 1_1/1_2 xx "r"_2^2/"r"_1^2`

`= 3/2 xx (3/2)^2`

`= (3)^3/(2)^3`

`= 27/8`

`therefore "I"_1/"I"_2 = ("V"//"R"_1)/("V"//"R"_2) = "R"_2/"R"_1 = 8/27`