## AC Generator or AC Dynamo

Subject: Physics

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#### Overview

An electrical machine used to convert mechanical energy into electrical energy is called A.C. generator. This note provides us an information on AC generator or Dynamo.

### AC Generator

An electrical machine used to convert mechanical energy into electrical energy is called A.C. generator.

#### Principle

It works on the principle of electromagnetic induction i.e. when a coil is rotated in a uniform magnetic field, an e.m.f is induced in it.

#### Construction

The main components of a.c. generator are:

1. Armature
Armature coil (ABCD) consists of a large number of turns of insulated copper wire wound over a soft iron core.
2. Strong field magnet
The armature is rotated in a strong uniform magnetic field provided by powerful permanent magnet NS. The axis of rotation is perpendicular to the field.
3. Slip rings
The two ends of the armature are connected to rings R1and R2.
4. Brushes
The two carbon brushes B1and B2are pressed against the slip rings. These brushes are connected to load and remain fixed while slip rings rotate along the armature.

#### Working

When the armature coil ABCD rotates in the magnetic field provided by the strong magnetic field. Magnetic flux is produced in the coil while cutting the magnetic lines of force. Hence e.m.f is induced in the coil. The direction of induced e.m.f or the current in the coil is determined by Fleming’s right-hand rule.

The current flows out through the brush B1in one direction of half of the revolution and through the brush B2in the next half revolution in the reverse direction. This process is repeated. Therefore, e.m.f produced is of alternating nature.

Theory

Consider the plane of the coil be perpendicular to the magnetic field $\vec B$. Let the coil be rotated anticlockwise with a constant angular velocity $\omega$. Then the angle between the normal to the coil and $\vec B$ at any time t is given by

$$\theta = \omega t$$

The component of the magnetic field normal to the plane of the coil = B\cos\: \theta = B\: \cos\: \omega t.\)

Magnetic flux linked with a single coil $= B\cos\:\omega t$ A where A is the area of the coil.

So, magnetic flux linked with N coils, $\phi = NBA\: \cos\: \omega t$.

From Faraday’s laws of electromagnetic induction, the induced e.m.f. in the coil is given by

\begin{align*} \epsilon &= - \frac {d\phi }{dt} = -\frac {d(NBA\: \cos \omega t)}{dt} \\ &= - NBA\frac {d}{dt}(\cos\: \omega t) = -NBA(\sin \: \omega t)\omega \\ \epsilon &= NBA\: \omega \: ]sin\: \omega t \dots (i) \\ \end{align*}

The magnitude of induced e.m.f. will be maximum i.e. $(\epsilon _0)$, when $\sin\: \omega t = 1,$ so

\begin{align*} \epsilon _0 &= NBA\omega \\ \text {Thus equation} \: (v)\: \text {becomes,} \\ \epsilon &= \epsilon _0 \sin \omega t \dots (i) \\ \text {The magnitude of induced e.m.f. is max when,}\: \sin\: \omega t = 1, \\ \epsilon _0 &= NBA\omega \\ \text {Equation} \: (v)\: \text {becomes,} \epsilon &= \epsilon _0 \sin\: \omega t \dots (ii) \\ \text {Instantaneous current is given by} \\ I &= \frac {\epsilon}{R} \\&= \frac {\epsilon _0 \sin\: \omega t}{R}\\ \text {where R is resistance of the coil} \\ \therefore I &= I_0 \sin \omega t \\ \text {where}\: \frac {\epsilon _0}{R} = I_0 \: \text {is maximum value} \\ \end{align*}

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, et al.Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.

##### Things to remember

An electrical machine used to convert mechanical energy into electrical energy is called A.C. generator.

AC generator works on the principle of electromagnetic induction i.e., when a coil is rotated in a uniform magnetic field, an e.m.f is induced in it.

The direction of induced e.m.f or the current in the coil is determined by Fleming’s right hand rule.

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