Question 79 of 380

Space between two concentric conducting spheres of radii $a$ and $b$ $(b\gt a)$ is filled with a medium of resistivity $\rho$ . The resistance between the two spheres will be:

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

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Answer: (C) $\dfrac{\rho }{4\pi }\left(\dfrac{1}{a}-\dfrac{1}{b}\right)$

Consider small volume element between $r$ and $r+dr$
Resistance of this volume along rational directions,
$dR=\dfrac{\rho dr}{4\pi {r}^{2}}$
As all element resistance are in series,
$R=\int _{r=a}^{r=b}\dfrac{\rho dr}{4\pi {r}^{2}}=\dfrac{\rho }{4\pi }{\left(-\dfrac{1}{r}\right)}_{r=a}^{r=b}=\dfrac{\rho }{4\pi }\left(\dfrac{1}{a}-\dfrac{1}{b}\right)$

JEE Main Physics practice question on Current Electricity (Resistance and Resistivity), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.