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 _____________ $$J$$.
A potentiometer wire of length $$300 \mathrm{~cm}$$ is connected in series with a resistance 780 $$\Omega$$ and a standard cell of emf $$4 \mathrm{V}$$. A constant current flows through potentiometer wire. The length of the null point for cell of emf $$20\, \mathrm{mV}$$ is found to be $$60 \mathrm{~cm}$$. The resistance of the potentiometer wire is ____________ $$\Omega$$.
As per given figures, two springs of spring constants $$k$$ and $$2 k$$ are connected to mass $$m$$. If the period of oscillation in figure (a) is $$3 \mathrm{s}$$, then the period of oscillation in figure (b) will be $$\sqrt{x}~ s$$. The value of $$x$$ is ___________.