Construction of an AC Generator
An AC generator converts mechanical energy into electrical energy based on electromagnetic induction.
It consists of:
1. Armature Coil (\( ABCD \)): A rectangular coil rotates inside a magnetic field.
2. Magnetic Field: Created using permanent magnets or electromagnets.
3. Slip Rings (\( S_1, S_2 \)): Connected to the coil, providing continuous contact.
4. Brushes: Connect the slip rings to the external circuit.

Working of an AC Generator
- The coil rotates in the magnetic field due to external mechanical energy.
- According to Faraday’s Law of Electromagnetic Induction, an EMF is induced: \[ \mathcal{E} = B L v \sin\theta \] - The induced current alternates because the coil changes orientation every half cycle.
- The output AC voltage follows: \[ \mathcal{E} = \mathcal{E}_0 \sin \omega t \]
The alternating current \( I \) in an inductor is observed to vary with time \( t \) as shown in the graph for a cycle.

Which one of the following graphs is the correct representation of wave form of voltage \( V \) with time \( t \)?}
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).