In a Wheatstone bridge (see fige ) Resitances P and Q are approximately equal .When `R= 400 Omega` the bridge is blanced .on is inerchanging P and Q ,the value of R, for balance is 405 `Omega ` .The value of X is close to :

Options

A. 404.5 ohm
B. 402.5 ohm
C. 403.5 ohm
D. 401.5 ohm

Answer

B

Explanation

Initially `P/a = (R_1)/(x)` .......(1)
After interchanging P and Q are
`Q/P = (R_2)/(x) `.......(2)
From (i) and (ii)
`1 - (R_1 R_2)/(x^2)`
`x = sqrt(R, R_2)`
`= sqrt(400 xx 405)`
`= 402.5 Omega`