If current '$$I$$' is flowing in the closed circuit with collective resistance '$$R$$', the rate of production of heat energy in the loop as we pull it along with a constant speed '$$\mathrm{V}$$' is ( $$\mathrm{L}=$$ length of conductor, $$\mathrm{B}=$$ magnetic field)

Two coils $$\mathrm{A}$$ and $$\mathrm{B}$$ have mutual inductance 0.008 $$\mathrm{H}$$. The current changes in the coil A, according to the equation $$\mathrm{I}=\mathrm{I}_{\mathrm{m}} \sin \omega \mathrm{t}$$, where $$\mathrm{I}_{\mathrm{m}}=5 \mathrm{~A}$$ and $$\omega=200 \pi ~\mathrm{rad} ~\mathrm{s}^{-1}$$. The maximum value of the e.m.f. induced in the coil $$B$$ in volt is

The mutual inductance (M) of the two coils is $$3 ~\mathrm{H}$$. The self inductances of the coils are $$4 ~\mathrm{H}$$ and $$9 ~\mathrm{H}$$ respectively. The coefficient of coupling between the coils is

The magnetic flux through a loop of resistance $$10 ~\Omega$$ varying according to the relation $$\phi=6 \mathrm{t}^2+7 \mathrm{t}+1$$, where $$\phi$$ is in milliweber, time is in second at time $$\mathrm{t}=1 \mathrm{~s}$$ the induced e.m.f. is