In Wheatstone's network P =` 2 Omega , Q = 2 Omega , R = 2 Omega and S = 3 Omega` The resistance with which S is to shunted in order that the bridge may be balanced is

Options

A. `2 Omega `
B. `6 Omega `
C. `1 Omega `
D. `4 Omega `

Answer

B

Explanation

Let X be the resistance with which S is to be shunted for the bridge to be balanced / Then , for balanced Wheatstone' bridge
`P/Q R/((SX)/(S+X)) " " ( :' "S and X are in parallel" ) `
Substituting the given values , we get
` (2Omega )/(2Omega ) = (2Omega )/(((3Omega)X)/(3Omega +X)) or ((3Omega)X)/(3Omega +X ) = 2Omega `
`(3 Omega ) X = (2 Omega ) (3 Omega ) + (2 Omega ) X `
` X (3 Omega - 2 Omega) = (2 Omega ) (3 Omega) `
` X ( 1 Omega ) = (2Omega ) (3 Omega)`
` X = ((2 Omega )(3 Omega))/(1 Omega ) = 6 Omega `