Draw a schematic sketch of an ac generator describing its basic elements. State briefly its working principle. Show a plot of variation of

(i) Magnetic flux and

(ii) Alternating emf versus time generated by a loop of wire rotating in a magnetic field.

#### Solution

Principle − Based on the phenomenon of electromagnetic induction.

**Construction:**

Main parts of an ac generator:

Armature − The rectangular coil ABCD

Filed Magnets − Two pole pieces of a strong electromagnet

Slip Rings − The ends of the coil ABCD are connected to two hollow metallic rings R_{1} and R_{2}.

Brushes − B_{1} and B_{2} are two flexible metal plates or carbon rods. They are fixed and are kept in tight contact with R_{1} and R_{2}, respectively.

**Working** − As the armature coil is rotated in the magnetic field, angle *θ* between the field and the normal to the coil changes continuously. Therefore, magnetic flux linked with the coil changes and an *emf* is induced in the coil. According to Fleming’s right hand rule, current is induced from A to B in AB and from C to D in CD. In the external circuit, current flows from *B*_{2} to *B*_{1}.

To calculate the magnitude of *emf* induced:

Suppose *A* → Area of each turn of the coil

*N* → Number of turns in the coil

`vecB`→ Strength of the magnetic field

θ → Angle which normal to the coil makes with `vecB` at any instant *t*

*∴ Magnetic flux linked with the coil in this position is given by,*

`phi=N(vecB.vecA)=NBAcostheta=NBAcos `

Where, ‘ω’ is angular velocity of the coil

Graph between magnetic flux and time, according to equation (i), is shown below:

As the coil rotates, angle *θ *changes. Therefore, magnetic flux *Φ* linked with the coil changes and an *emf* is induced in the coil. At this instant* t*, if *e* is the *emf* induced in the coil, then

`e=(dtheta)/dt=-d/dt(NABcos`

`=-NABd/dt(cos `

=-NAB(-sin *ωt*)*ω*

∴ e = NAB ω sin ωt

The graph between alternating emf versus time is shown below: