An unknown resistance r si determined in terms of a standared resistance `R = 100 Omega` by using potentiometer. The potential difference across r is balanced againt `45 cm` length of the wire and that `(r + R)` is obtained at `70 cm` of the wire. Find the value of the unknown resistance.

Options

A. `200 Omega`
B. `280 Omega`
C. `180 Omega`
D. `100 Omega`

Answer

C

Explanation

`l_(1) = 45 cm, l_(2) = 70 cm`
`R = 100 Omega`
`r = R ((l_(1))/(l_(2) - l_(1))) = 100 ((45)/(75 - 45)) = 180 Omega`