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

Rate of heat flow, `Q/t = (KAdeltathetaT)/(l)`
`rArr (K_(A)/K_(B)) = (A_(B))/A_(B)) = (r_(B)/r_(A))^(2) = 1/4 rArr K_(A) = K_(B)/4`