The frequencies at which the current amplitude in an LCR series circuit becomes $$\frac{1}{\sqrt{2}}$$ times its maximum value, are $$212\,\mathrm{rad} \,\mathrm{s}^{-1}$$ and $$232 \,\mathrm{rad} \,\mathrm{s}^{-1}$$. The value of resistance in the circuit is $$R=5 \,\Omega$$. The self inductance in the circuit is __________ $$\mathrm{mH}$$.

A conducting circular loop is placed in $$X-Y$$ plane in presence of magnetic field $$\overrightarrow{\mathrm{B}}=\left(3 \mathrm{t}^{3} \,\hat{j}+3 \mathrm{t}^{2}\, \hat{k}\right)$$ in SI unit. If the radius of the loop is $$1 \mathrm{~m}$$, the induced emf in the loop, at time, $$\mathrm{t}=2 \mathrm{~s}$$ is $$\mathrm{n} \pi \,\mathrm{V}$$. The value of $$\mathrm{n}$$ is ___________.

To light, a $$50 \mathrm{~W}, 100 \mathrm{~V}$$ lamp is connected, in series with a capacitor of capacitance $$\frac{50}{\pi \sqrt{x}} \mu F$$, with $$200 \mathrm{~V}, 50 \mathrm{~Hz} \,\mathrm{AC}$$ source. The value of $$x$$ will be ___________.

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 _____________ $$J$$.