A resistance of `2Omega` is connected across one gap of a metre-bridge(the length of the wire is 100 cm) and an unknown resistance, greater than `2Omega`, is connected across the other gap. When these resistances are interchanged, the balance points shifts by 20 cm. Neglecting any corrections, the unknown resistance is

Options

A. `3Omega`
B. `4Omega`
C. `5Omega`
D. `6Omega`

Answer

A

Explanation

(a) Given X is greater than `2Omega` when the bridge is balanced.
`R/l = X/(100-l)`

.Case (i)
or `100R - Rl = lX or, 200-2l = lX`
or, `l = 200/(X+2)`
When the resistance are interchanged the jockey shifts
20 cm. Therefore,
`X/(l+20) = 2/(80 -l)`
`80 X - l X = 2l + 40 `
or , `80X = l(X + 2) + 40 `
or, `80X = (200/ (X+2)) (X+2) + 40`
or, `X = (240/80) = 3Omega` .