The wire AB of a meter bridge changes linearly from radius r to 2r from left end to right end. Where should the free end of the galvanometer be connected on AB so that the deflection in the galvanometer is zero.
Text Solution
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Sol. Let the galvanometer be connected at a point x = x, from end A where x = 0.
Let R 1 = resistance of left part i.e. Ax, and
R 2 = resistance of right part i.e. x, B
Length = 100 cm = 1m
Consider an element of thickness dx at a distance x from end A and of radius r x .
Thus r x = 
= r (1 + x)
Resistance of this element = dRx = 
R 1 = 
= 
R x = 
= 
For null point of zero deflection.
= 
= 1 ⇒ 1 – 
= 
– 
x 1 = 
= 33.33 cm.
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