JEE PYQ: Current Electricity Question 51
Question 51 - 2019 (10 Apr 2019 Shift 2)
Space between two concentric conducting spheres of radii $a$ and $b$ ($b > a$) is filled with a medium of resistivity $p$. The resistance between the two spheres will be:
(1) $\frac{p}{4\pi}\left(\frac{1}{a} - \frac{1}{b}\right)$
(2) $\frac{p}{2\pi}\left(\frac{1}{a} - \frac{1}{b}\right)$
(3) $\frac{p}{2\pi}\left(\frac{1}{a} + \frac{1}{b}\right)$
(4) $\frac{p}{4\pi}\left(\frac{1}{a} + \frac{1}{b}\right)$
Show Answer
Answer: (1)
Solution
$dR = \frac{p,dx}{4\pi x^2}$. $R = \int_a^b \frac{p}{4\pi x^2},dx = \frac{p}{4\pi}\left[-\frac{1}{x}\right]_a^b = \frac{p}{4\pi}\left(\frac{1}{a} - \frac{1}{b}\right)$.
BETA
