Wires A and B have have identical lengths and have circular cross-sections. The radius of A is twice the radius of B i.e. `R_A = 2R_B`. For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by-

Options

A. `K_(A)= 4K_(B)`
B. `K_(A)=2K_(B)`
C. `K_(A)=K_(B)//2`
D. `K_(A)=K_(B)//4`

Answer

D

Explanation

We use `r=(Q)/(T)=(kADeltaT)/(L)`
As `r_(A)=r_(B)`
`implies K_(A)A_(A)=K_(B)A_(B)`
`implies K_(A)piR_(A)^(2)=K_(B)piR_(B)^(2)`
`implies K_(A)(2R_(B))^(2)=K_(B)R_(B)^(2)`
`implies K_(A)=(K_(B))/(4)`