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Question: A thick spherical shell has inner radius b and outer radius a. The material has resistivity r. It's ...

A thick spherical shell has inner radius b and outer radius a. The material has resistivity r. It's resistance between inner and outer surface is –

A

ρ(b−a)4πab\frac{\rho(b - a)}{4\pi ab}

B

ρ(b−a)4ab\frac{\rho(b - a)}{4ab}

C

ρ(a−b)4ab\frac{\rho(a - b)}{4ab}

D

ρ(a−b)4πab\frac{\rho(a - b)}{4\pi ab}

Answer

ρ(a−b)4πab\frac{\rho(a - b)}{4\pi ab}

Explanation

Solution

At radius r

E = rJ

– dVdr\frac{dV}{dr} = ρi4πr2\frac{\rho i}{4\pi r^{2}}

∫r=br=adrr2\int_{r = b}^{r = a}\frac{dr}{r^{2}}

v1−v2i\frac{v_{1} - v_{2}}{i} = ρ4π\frac { \rho } { 4 \pi } (a−bab)\left( \frac{a - b}{ab} \right)

\ R = ρ4π(a−b)ab\frac{\rho}{4\pi}\frac{(a - b)}{ab}