Question

Draw a labeled diagram of AC generator.Derive the expression for the instantaneous value of the emf induced in the coil.

Answer 1

Construction of AC generator:

Main parts of an AC generator include,

1. Armature-Rectangular coil ABCD.

2. Field magnet

3. Slip Rings

4. Brushes $B_1,B_2$

Working: As the armature coil is rotated in magnetic field,angle $\theta$ between the field and normal to the coil changes continuously ,therefore magnetic flux linked with the coil changes.An emf is induced in the coil.According to Fleming’s right hand rule,to calculate emf,Suppose,

$A$-Area of each turn the coil.

$N$-Number of turn in the coil.

$\overrightarrow{B}$-strength of magnetic field.

$\theta$-angle which normal to the coil make with $\overrightarrow{B}$ at any instant t.

Magnetic Flux linked with coil in this position.

$\varphi =N(\overrightarrow{B}.\overrightarrow{A})=NBA\cos \theta$

$=NBA\cos \omega t$

$e=-\frac{d\varphi }{dt}=-NBA(-\left(\sin \omega t\right)\omega )$

$e=+NBA\omega \sin \omega t$