The flux linked with a coil at any instant $$'t'$$ is given by
$$\phi = 10{t^2} - 50t + 250$$
The induced $$emf$$ at $$t=3s$$ is

An inductor $$(L=100$$ $$mH)$$, a resistor $$\left( {R = 100\,\Omega } \right)$$ and a battery $$\left( {E = 100V} \right)$$ are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circuiting the points $$A$$ and $$B$$. The current in the circuit $$1$$ $$ms$$ after the short circuit is

A coil of inductance $$300$$ $$mH$$ and resistance $$2\,\Omega $$ is connected to a source of voltage $$2$$ $$V$$. The current reaches half of its steady state value in

One conducting $$U$$ tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field $$B$$ is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed $$v,$$ then the $$emf$$ induced in the circuit in terms of $$B,l$$ and $$v$$ where $$l$$ is the width of each tube, will be