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

Let x be the unknown resistance.
In first case, when Wheatstone bridge is balanced,we get
`(2)/(x)=(1)/((100-l))" "…(i)`
In second case, when Wheatstone bridge is balanced, then
`(x)/(2)=(l+20)/(80-l)" "…(ii)`
Solving equations (i) and (ii), we get `x=3Omega`