In a coil of resistance $$8 \,\Omega$$, the magnetic flux due to an external magnetic field varies with time as $$\phi=\frac{2}{3}\left(9-t^{2}\right)$$. The value of total heat produced in the coil, till the flux becomes zero, will be _____________ $$J$$.

The effective current I in the given circuit at very high frequencies will be ___________ A.

Magnetic flux (in weber) in a closed circuit of resistance 20 $$\Omega$$ varies with time t(s) at $$\phi$$ = 8t² $$-$$ 9t + 5. The magnitude of the induced current at t = 0.25 s will be ____________ mA.

A series LCR circuit with $$R = {{250} \over {11}}\,\Omega $$ and $${X_L} = {{70} \over {11}}\,\Omega $$ is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be _________ $$\mu$$F. (Take : $$\pi = {{22} \over 7}$$)