Question

There are two concentric spheres of radius $a$ and $b$ respectively. If the space between them is filled with medium of resistivity $\rho$, then the resistance of the inter gap between the two spheres will be

• A. $\frac{\rho }{4\pi (b+a)}$
• B. $\frac{\rho }{4\pi }\left(\frac{1}{b}-\frac{1}{a}\right)$
• C. $\frac{\rho }{4\pi }\left(\frac{1}{a^2}-\frac{1}{b^2}\right)$
• D. $\frac{\rho }{4\pi }\left(\frac{1}{a}-\frac{1}{b}\right)$

Answer 1

Answer: (D)

Consider a concentric spherical shell of radius $x$ and thickness $dx$ as showing in figure. Its resistance, $dR$ is $dR=\frac{\rho dx}{4\pi x^2}$

$\therefore$ Total resistance, $R=\frac{\rho }{4\pi }\frac{dx}{x}=\frac{\rho }{4\pi }\left(\frac{1}{a}-\frac{a}{b}\right)$