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A resistance of 2Omega is connected acro...

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

A

`3Omega`

B

`4Omega`

C

`5Omega`

D

`6 Omega`

Text Solution

Verified by Experts

The correct Answer is:
A
a. Given X is greater than `2Omega` when the bridge is balanced.

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