Wires A and B have identical lengths and have circular cross-sections. The radius of A is twice the radius of B \[i.e.\] \[{{r}_{A}}=2{{r}_{B}}\]. 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

• A.   \[{{K}_{A}}=4{{K}_{B}}\] 
• B.   \[{{K}_{A}}=2{{K}_{B}}\]
• C.   \[{{K}_{A}}={{K}_{B}}/2\]
• D.   \[{{K}_{A}}={{K}_{B}}/4\]