Current Electricity 1 Question 1

1. Space between two concentric conducting spheres of radii a and b(b>a) is filled with a medium of resistivity ρ. The resistance between the two spheres will be

(a) ρ2π1a+1b

(b) ρ4π1a1b

(c) ρ2π1a1b

(d) ρ4π1a+1b

(2019 Main, 10 April II)

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Solution:

  1. Key Idea Resistance between surface of inner shell and a circumferential point of outer shell can be formed by finding resistance of a thin (differentially thin) shell in between these two shells. Then, this result can be integrated (summed up) to get resistance of the complete arrangement.

For an elemental shell of radius x and thickness dx,

Resistance, dR=ρlA

dR=ρdx4πx2

So, resistance of complete arrangement is

R=abdR=abρdx4πx2=ρ4πabx2dxR=ρ4πx11=ρ4π1xab=ρ4π1b1a=ρ4π1a1b ohm 



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