$A$ circular coil of area $0.01 \ m^2$ and $40$ turns is rotated about its vertical diameter with an angular speed of $50 \ rad \ s^{-1}$ in a uniform horizontal magnetic field of $0.05 \ T$. If the average power loss due to Joule heating is $25 \ mW$,then the closed loop resistance of the coil is: (in $Omega$)

What is the phase difference between the flux linked with a coil rotating in a magnetic field and the induced emf produced in it?

Write the equation for the maximum $emf$ in an $AC$ generator.

Discuss the characteristics of the induced $emf$ in an $AC$ generator.

At the centre of a fixed large circular coil of radius $R$,a much smaller circular coil of radius $r$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current $I$. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the $emf$ induced in the smaller coil after a time $t$ of its start of rotation.

$A$ ring of resistance $10 \Omega$,radius $10 \text{ cm}$,and $100$ turns is rotated at a rate of $100$ revolutions per second about a fixed axis which is perpendicular to a uniform magnetic field of induction $10 \text{ mT}$. The amplitude of the current in the loop will be nearly $A$ (Take $\pi^2 = 10$).