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 \( I\) 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 \(0°C\).

The time at which sphere attains half of its maximum attainable temperature is \(\frac{c}{k}\ln 2^a\). Then find the value of "\(a\)".

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