Sign in
Please select an account to continue using cracku.in
↓ →
A solid cylinder, made up of a material of resistivity $$\rho$$, has length $$\ell$$ and radius $$r\sqrt{3}$$. Three coaxial cylinders A, B and C of equal length $$\ell$$ have been cut from this thick cylinder. The cylinder A is a solid cylinder of radius r. B is a hollow cylinder with inner radius r and uniform wall thickness $$(\sqrt{2} - 1)r$$ while the hollow cylinder C has inner radius $$r\sqrt{2}$$ and outer radius $$r\sqrt{3}$$. The relationship between their end-to-end resistance is
End-to-end resistance is $$R = \frac{\rho\ell}{A}$$, so with equal lengths only the cross-sectional areas matter. A has area $$\pi r^2$$. B has outer radius $$r + (\sqrt{2} - 1)r = \sqrt{2}r$$, so its area is $$\pi(2r^2 - r^2) = \pi r^2$$, and C has area $$\pi(3r^2 - 2r^2) = \pi r^2$$. All areas are equal, so $$R_A = R_B = R_C$$.
Was this solution helpful?
Predict your JEE Main percentile, rank & performance in seconds
Educational materials for JEE preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.
91- 6303239042
