A highly conducting uniform sphere of thermal capacity C is heated by an electric heater, a resistance R fitted within the sphere. A constant current is passed through the heater starting at time $t=0$ which gives constant power. The sphere loses heat at a rate equal to k times the temperature difference between the sphere and the surrounding. The initial temperature of the sphere and that of the surrounding is  $0^{\circ }C$. The time at which sphere attains half of its maximum attainable temperature is  $\frac{c}{k}\mathcal{l}n{2}^a$. Then find the value of ‘’a’’.