(a) Draw a schematic diagram of an AC generator. Explain is working and obtain the expression for the instantaneous value of the emf in terms of the magnetic field B, number of turns N of the coil of area A rotating with angular frequency `omega`. Show how an alternating emf is generated by loop of wire rotating in a magnetic field.
(b) A circular coil of radius 10 cm and 20 turns is rotated about its vertical diameter with angular speed of 50 rad `s^(-1).` in a uniform horizontal magnetic field of `3.0xx10^(-2)T`.
(i) Calculate the maximum and average emf induced in the coil.
(ii) If the coil forms a closed loop of resistance `10 Omega`, calculate the maximum current in the coil and the average power loss due to Joule heating.

Explanation

### Solution:

#### Part (a): Schematic Diagram and Working of an AC Generator

1. **Schematic Diagram**:
- Draw a rectangular coil (labeled ABCD) placed between the poles of a magnet (labeled N and S).
- Indicate the direction of rotation of the coil using an arrow.
- Show slip rings connected to the ends of the coil and brushes that make contact with the slip rings.
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