# Space between two concentric conducting spheres of radii a and  b (b>a) is filled with a medium of resistivity $\rho$. The resistance between the two spheres will be : Option 1) $\frac{\rho }{4\pi }\left ( \frac{1}{a} -\frac{1}{b}\right )$ Option 2) $\frac{\rho }{2\pi }\left ( \frac{1}{a} -\frac{1}{b}\right )$ Option 3) $\frac{\rho }{2\pi }\left ( \frac{1}{a} +\frac{1}{b}\right )$ Option 4) $\frac{\rho }{4\pi }\left ( \frac{1}{a} +\frac{1}{b}\right )$

Answers (1)

Take a shell at distnce r from centre and find out its Resistance .

$R= \int_{0}^{R}dR=\int_{a}^{b}\frac{\rho dr}{4\pi r}$

$=\frac{\rho }{4\pi }\left [ \frac{1}{a}-\frac{1}{b} \right ]$

Option 1)

$\frac{\rho }{4\pi }\left ( \frac{1}{a} -\frac{1}{b}\right )$

Option 2)

$\frac{\rho }{2\pi }\left ( \frac{1}{a} -\frac{1}{b}\right )$

Option 3)

$\frac{\rho }{2\pi }\left ( \frac{1}{a} +\frac{1}{b}\right )$

Option 4)

$\frac{\rho }{4\pi }\left ( \frac{1}{a} +\frac{1}{b}\right )$

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