State the principle of a transformer. Explain its construction and working. Derive an expression for the ratio of e.m.f's in terms of number of turns in primary and secondary coil.
Two diametrically opposite points of a metal ring are connected to two terminals of the left gap of meter bridge. The resistance of `11Omega` is connected in right gap. If null point is obtained at a distance of 45 cm from the left end, find the resistance of metal ring.

Explanation

Numerical :
Given : `R_(2)=11Omega,l_(1)=45" cm",l_(2)=100-45=55" cm"`
Resistance of metal ring `(R_(1))=?`
`(R_(1))/(R_(2))=(l_(1))/(l_(2))`
Resistance of each half segment of the metal ring `=(R_(1))/(2)`.
These half segments are connected in parallel in the left gap.
`R_(eff.)=((R_(1))/(2)xx(R_(1))/(2))/((R_(1))/(2)+(R_(1))/(2))=((R_(1))/(2)xx(R_(1))/(2))/(R_(1))=(R_(1)^(2))/(4R_(1))`
`R_(eff.)=(R_(1))/(4)Omega`
From the formula,
`(R_(eff.))/(R_(2))=(l_(1))/(l_(2))`
`((R_(1))/(4))/(11)=(45)/(55)`
`(R_(1))/(44)=(45)/(55)`
`R_(1)=(45)/(55)xx44`
`R_(1)=36Omega`
`:.` The resistance of metal ring is `36Omega`.