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Question

Two long coaxial and conducting cylinders of radius a and b are separated by a material of conductivity σ and a constant potential difference V is maintained between them. Then the current, per unit length flowing in between cylinders is

A
4πσln(ba)V
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B
4πσ(b+a)V
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C
2πσln(ba)V
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D
2πσ(b+a)V
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Solution

The correct option is C 2πσln(ba)VResistance of the small cylindrical element of thickness dx is dR=dxσdA=dxσ2πxl As each element is in series Reff=∫dR=∫badxσ2πxl=12πσlln(b/a) From Ohms law, I=VR=V12πσlln(b/a) I=2πσlVln(ba) Current per unit length is Il=2πσVln(ba) Why this Question? Tip: Use of integration for finding effective resistance is significant for JEE.

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