A cylinder of radius r made of a material of thermal conductivity `K_(1) = K` is surrounded bt cylendrical shell of inner radius R and outer radius 3R made of a material of thermal conductivity `K_(2) = 2K`. The two ends of the combined system are maintained at two different temperatures .
there is no loss of heat across the cylendrical surface and system is in steadt state . what is the effective thermal conductivity of the system ?

Options

A. `K_(1)+K_(2)`
B. `(K_(1)K_(2))/((K_(1)+K_(2)))`
C. `((K_(1)+3K_(2))/(4))`
D. `((3K_(1)+K_(2))/(4))`

Answer

C

Explanation

Let `R_(1) and R_(2)` be the thermal resistance of inner and outer portions since temperature difference at both ends is same, the resistances are in parallel. Hence,
`(1)/(R)=(1)/R_(2)+(1)/(R_(2))`
`(K(4piR^(2)))/(l)=(K_(1)(piR^(2)))/(l)+(K_(2)(3piR^(2)))/(l)rArrK=(3K_(2)+K_(1))/(4)`