Question

A piece of wire of resistance R is cut into three equal parts. These parts are then connected in parallel. If the equivalent resistance of this parallel combination is R₁, what is the value of the ratio R₁ : R?

Answer 1

The resistance of each part is `"R"/3` Ω (as resistance is proportional to the length of the wire.)

`1/"R"_1 = 3/"R" + 3/"R" + 3/"R"`

`1/"R"_1= (3 + 3 + 3)/"R"`

`1/"R"_1= 9/"R"`

∴ `"R"_1 = "R"/9`

∴ `"R"_1/"R" = 1/9`

Answer 2

The resistance of each part is `"R"/3` Ω (as resistance is proportional to the length of the wire.)

`1/"R"_1 = 3/"R" + 3/"R" + 3/"R"`

`1/"R"_1= (3 + 3 + 3)/"R"`

`1/"R"_1= 9/"R"`

∴ `1/"R"_1 = 9/"R"`

∴ `"R"/"R"_1 = 9`