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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