In an $$AC$$ generator, a coil with $$N$$ turns, all of the same area $$A$$ and total resistance $$R,$$ rotates with frequency $$\omega $$ in a magnetic field $$B.$$ The maximum value of $$emf$$ generated in the coil is

In a series resonant $$LCR$$ circuit, the voltage across $$R$$ is $$100$$ volts and $$R = 1\,k\Omega $$ with $$C = 2\mu F.$$ The resonant frequency $$\omega $$ is $$200$$ $$rad/s$$. At resonance the voltage across $$L$$ is

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

The refractive index of a glass is $$1.520$$ for red light and $$1.525$$ for blue light. Let $${D_1}$$ and $${D_2}$$ be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then,