Resistance of ....

Electricity and Magnetism Level 3

There are two concentric sphere of radius 3m and 5m respectively. If the space between them is filled with medium of resistivity 360π .Then resistance of the inner gap between two spheres will be....


The answer is 12.

Gaurav Yogeshwar by Gaurav Yogeshwar , 25, India

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2 solutions

Chew-Seong Cheong
Aug 20, 2014

The increment in resistance Δ R \Delta R at a sphere with radius r r , where 3 ≤ r ≤ 5 3 \le r \le 5 is given by:

Δ R = ∫ 3 5 360 π d r 4 π r 2 = 90 ∫ 3 5 d r r 2 = 90 [ − 1 r ] 3 5 \Delta R = \int_{3}^{5}{\frac{360\pi dr}{4\pi r^2}}= 90\int_{3}^{5}{\frac{dr}{r^2}}= 90\left[-\cfrac{1}{r}\right]_3^5

= 90 [ − 1 5 + 1 3 ] = 90 [ 2 15 ] = 12 Ω \quad \quad = 90\left[-\cfrac{1}{5}+\cfrac{1}{3}\right] = 90\left[\cfrac{2}{15}\right]= \boxed{12\Omega}

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Consider a sphere of radius r between two given spheres. Use v=E.dx and I=J.ds then, do simple integration

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