Write a Narrative essay of HL (150-200) & FAL (130-180) words on one of the topics listed below: 1. A life lesson you have learned 2. A frightening or dangerous experience you had. 3. An encounter with a stranger that left a lasting impact.

Step 1: Principle of operation based on electromagnetic induction.

The AC generator works on Faraday's law of electromagnetic induction. When the rectangular coil (armature) rotates in the uniform magnetic field between the north (N) and south (S) poles, the magnetic flux through the coil changes, inducing an emf.

Step 2: Magnetic flux through the coil.

Consider a coil with $N$ turns, each of area $A = l \times b$ (length $l$, breadth $b$), in magnetic field $B$. Assume the field is perpendicular to the plane of the coil at $t=0$.

Magnetic flux $\phi$ through one turn: $\phi = B A \cos \theta$

where $\theta$ is the angle between the magnetic field $\mathbf{B}$ and the normal to the plane of the coil.

For $N$ turns: $\Phi = N B A \cos \theta$

The coil rotates with constant angular velocity $\omega$, so $\theta = \omega t$.

Substitute: $\Phi = N B A \cos (\omega t)$

Units: $\Phi$ in Wb (webers), $B$ in T, $A$ in m², $\theta$ dimensionless.

Step 3: Induced emf using Faraday's law.

$\epsilon = -\frac{d\Phi}{dt}$

Differentiate $\Phi$: $\frac{d\Phi}{dt} = N B A \frac{d}{dt} [\cos (\omega t)] = N B A (-\omega \sin (\omega t))$

So, $\epsilon = - [N B A (-\omega \sin (\omega t))] = N B A \omega \sin (\omega t)$

Units: $\epsilon$ in V, $\omega$ in rad/s.

Step 4: Instantaneous and peak emf.

Instantaneous emf: $\epsilon(t) = \epsilon_0 \sin (\omega t)$

where peak emf $\epsilon_0 = N B A \omega$.

The emf alternates direction every half cycle (period $T = \frac{2\pi}{\omega}$), producing alternating current (AC) in the external circuit via slip rings and brushes.

Step 5: Output to the bulb.

The alternating current flows through the slip rings, carbon brushes, and the bulb, causing it to light up due to heating effect of the current.

Final answer: Induced emf is $\epsilon = NBA\omega \sin(\omega t)$ V

\epsilon = NBA\omega \sin(\omega t)