In a metere bridge, the wire consists of two parts one of length 30 cm and of radius r and the other of radius 2r. Where will the null point occur if the resistance in the left and right gaps are `5Omega` and `8Omega` respectively? The material of the wires is the same.

Answer

18.3 cm

Explanation

We have `("left gap resistance")/("right gap resistance")=(5)/(8)=0.625`
`("left length resistance")/("right length resistance")=((30)/(r^(2)))/((70)/(4r^(2)))=1.7`
Hence the null point is on the thin wire. Let it be at a distance x.
Then `(5)/(8)=(rhoxx(x))/((pir^(2))/(rhoxx((30-x))/(pir^(2))+(rho70)/(pi4r^(2))))=(4x)/(190-4x)`
or `x=18.3cm`