Question

The wire AB of length 100 cm 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 ?

• A. 33.33 cm
• B. 17.33 cm
• C. 17.33 cm
• D. 5.33 cm

Answer 1

Answer: (A)

33.33 cm

Answer 2

Radius of element = r +$\frac{rx}{1}$= $r(1 + x)$

Resistance of this element dR_x =$\frac{\rho dx}{\pi(1 + x)^{2}r^{2}}$

R₁ =$\int_{0}^{x_{1}}{dR_{x}}$R₂ = $\int_{x_{1}}^{1}{dR_{x}}$

For null point ,$\frac{R_{1}}{R_{2}} = \frac{4}{1}$and solve for x₁.