(a) State the principle of an ac generator and explain its working with the help of a labelled diagram. Obtain the expression for the emf induced in a coil having N turns each of cross-sectional area A, rotating with a constant angular speed ω in a magnetic field $\overrightarrow{\mathrm{B}}$, directed perpendicular to the axis of rotation.

(b) An aeroplane is flying horizontally from west to east with a velocity of 900 km/ hour. Calculate the potential difference developed between the ends of its wings having a span of 20 m. The horizontal component of the Earth’s magnetic field is 5 × 10^-4 T and the angle of dip is 30°.

OR

A device X is connected across an ac source of voltage V = V₀ sin ωt . The current through X is given as I = I₀ sin (ωt+π2)
(a) Identify the device X and write the expression for its reactance.

(b) Draw graphs showing variation of voltage and current with time over one cycle of ac,
for X.

(c) How does the reactance of the device X vary with frequency of the ac? Show this
variation graphically.

(d) Draw the phasor diagram for the device X.

$\mathrm{V}={\mathrm{V}}_0\sin \mathrm{\omega t};\mathrm{I}={\mathrm{I}}_0\sin \left(\mathrm{\omega t}+\frac{\mathrm{\pi }}{2}\right)$.