The a.c generator consists of:

- an armature- a rectangular coil consisting of a large number of an insulated wire wound on a laminated soft iron core
- a magnetic field- created by the curved poles ofÂ a horse shoe magnet or an electromagnetÂ
- two copper slip rings R
_{1}, R_{2}– to which ends of rectangular coils are connected and which rotate with the armature - two stationary carbon brushes : which are made to press lightly against the slip rings Â

An alternating voltage whose waveform is obtained above at the terminals by means of carbon brushes and slip rings

If the coil of area A rotates in magnetic field of strength B. Let the normal to the coil make an angle Î¸ with the field as shown,

Flux Î¸ through the coil is given by Ï† = ABCosÎ¸ ________(1)

If there are N number of turns in the coil, then, Ï† = NABcosÎ¸ _________(2)

If the coil turns with a steady angular velocity Ï‰ is given by

Ï‰ = \( \frac{dÎ¸}{dt} \) _________(3)

the induced e.m.f is given byÂ

E =Â \( \frac{- dÎ¸}{dt} \) _________(4)

The above equation follows from Faradayâ€™s and Lenzâ€™s laws

E =Â \( \frac{- dÎ¸}{dt} = \frac{- d}{dt} \scriptsize (NABcosÎ¸) \)Â

E = \( \scriptsize – NAB Â \normalsize \frac{ d}{dt} \scriptsize (cosÎ¸) \)

E =Â \( \scriptsize NAB sinÎ¸ Â \normalsize \frac{ dÎ¸}{dt} \) _______(5)Â Â

From equation (3) Â Ï‰ = \( \frac{dÎ¸}{dt} \)Â

âˆ´ E = NABÏ‰ sinÎ¸ __________(6), if Î¸ = 90 , then equation 6 becomes

Â E = NABÏ‰ = E_{O }___________(7)

where E_{O} is the maximum induced e.m.f which occurs when the coil is parallel to the field direction.

E = E_{O}sinÎ¸, but Ï‰ = \( \frac{dÎ¸}{dt} \), Î¸ =Â Ï‰t

Â E = E_{O}sinÏ‰ t ______________(8)

Alternating current a.c is a current which changes continually in direction while passing through a conductor

**Measurement of A.C**

An a.c can be measured by:

Hot-wire ammeter- using the heating effect of current

Moving iron ammeter- using the magnetic field of current

Moving coil galvanometer to which a rectifier is attached to convert a.c to d.c

## Responses