At the center 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 their smaller coil after a time t of its start of rotation.

A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 $$ \times $$ 10^-2 m. The magnetic field at the center of the triangle will be :

A capacitor C₁ = 1.0 $$\mu $$F is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now C₁ is disconnected from battery and connected to a circuit consisting of two uncharged capacitors $${C_2} = 3.0\mu F$$ and C₃ = 6.0 $$\mu $$F through switch (2), as shown in the figure. The sum of final charges on C₂ and C₃ is :

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lenses is $$2$$ cm. The focal lengths of the component lenses are :