A copper cylindrical tube has inner radius a and outer radius b. The resistivity is ρ. The resistance of the cylinder between the two ends is
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?

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Answers

Bs Academy
Feb 13, 2022
If one had considered a solid cylinder of radius b, one can suppose that it is made of two concentric cylinders of radius a and the outer part, joined along the length concentrically one inside the other.
If Ia and Ix are the currents flowing through the inner and outer cylinders
∵ Itotal = Ib = Ia + Ix
⇒ VRb = V/Ra + V/Rx
where Rb is the total resistance and Rx is the resistance of the tubular part.
∴  
But 
∴ 
∴ 

If one had considered a solid cylinder of radius b, one can suppose that it is made of two concentric cylinders of radius a and the outer part, joined along the length concentrically one inside the other.If Ia and Ix are the currents flowing through the inner and outer cylinders Itotal = Ib = Ia + Ix⇒ VRb = V/Ra + V/Rxwhere Rb is the total resistance and Rx is the resistance of the tubular part.∴But∴∴
If one had considered a solid cylinder of radius b, one can suppose that it is made of two concentric cylinders of radius a and the outer part, joined along the length concentrically one inside the other.If Ia and Ix are the currents flowing through the inner and outer cylinders Itotal = Ib = Ia + Ix⇒ VRb = V/Ra + V/Rxwhere Rb is the total resistance and Rx is the resistance of the tubular part.∴But∴∴