Question

A piece of wire of resistance ‘R’ is cut lengthwise into three identical parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the value of `R/(R')` is ______.

Options

• `1/9`

• `1/3`

• 3

• 9

Answer 1

A piece of wire of resistance ‘R’ is cut lengthwise into three identical parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the value of `R/(R')` is 9.

Explanation:

The resistance of one wire is ‘R’ divided into 3 resistances, which are `R/3` connected in parallel.

The equivalent resistance `1/(R') =  1/(R/3) + 1/(R/3) + 1/(R/3)`

Hence, `1/(R') = 3/R + 3/R + 3/R`

`1/(R') = 9/R`

⇒ R' = `R/9`

⇒ `R/(R')` = 9