With an unknown resistance X in the left gap and a resistance R in the right gap of a meter bridge, the neutral point is obtained at a distance of 75cm from the left end. The shift of null point if the unknown resistance is shunted by an equal resistance X and keeping same resistance in right gap is

Explanation

Data: `R=30 Omega, L_(X) = 40 cm`,
`L_(R) = 100- L_(X)= 60 cm`
(i) With the resistance X in the left gap and R`= 30 Omega` in the right gap
`X/R= L_(X)/L_(R)`
`therefore` The unknown resistance is,
`X=R(L_(X))/L_(R) = 30 xx 40/60 = 20 Omega`
(ii) When the resistance in each gap is increased by `15Omega`, the resistance in the left gap is
`X'=X +15=20+15 = 35 Omega`, and the resistance in the right gap is
`R'=R+ 15= 30 + 15 = 45 Omega`
`therefore X^(')/R^(') = L_(X)^(')/L_(R)^(')`
`therefore (L_(X)^('))/(100 - L_(X)^(')) = (35/45) = 7/9`
`therefore 9 L_(X)^(') = 700- 7 L_(X)^(') therefore 16 L_(X)^(') = 700`
`therefore L_(X)^(') = 700/16=43.75` cm
Since, `L_(X)^(') gt L_(X)`, the null point shifts to the right by
`L_(X)^(') - L_(X)= 43.75 cm - 40 cm = 3.75` cm