Question

The space between two coaxial cylinders whose radii a and b (where a < b) as shown in figure, is filled with a conducting medium. The specific conductivity of the medium is s. s= $\frac { \sigma _ { 0 } } { \mathbf { r } }$ , where r is radial distance from common axis of both cylinder. Assuming L >> b, where L is the length of cylinder –

• A.
• B.
• C. $\frac { \mathrm { b } - \mathrm { a } } { \pi \mathrm { L } \sigma _ { 0 } }$
• D. $\frac { \mathrm { b } - \mathrm { a } } { 6 \pi \mathrm { L } \sigma _ { 0 } }$

Answer 1

Answer: (B)

Answer 2

Consider a cylinder of radius r and thickness dr

dR = $\frac { \rho . \mathrm { dr } } { 2 \pi \mathrm { rL } }$

=

dR =

Resistance = $\int _ { \mathrm { r } = \mathrm { a } } ^ { \mathrm { r } = \mathrm { b } } \mathrm { dR }$

=