State the working of a.c. generator with the help of a labelled diagram.

The coil of an a.c. generator having N turns, each of area A, is rotated with a constant angular velocity. Deduce the expression for the alternating e.m.f. generated in the coil.

What is the source of energy generation in this device?

OR

(a) Show that in an a.c. circuit containing a pure inductor, the voltage is ahead of current by /2 in phase.

(b) A horizontal straight wire of length L extending from east to west is falling with speed v at right angles to the horizontal component of Earth’s magnetic field B.

(i) Write the expression for the instantaneous value of the e.m.f. induced in the wire.

(ii) What is the direction of the e.m.f.?

(iii) Which end of the wire is at the higher potential?

Working of ac generator:

When the armature coil is rotated in the strong magnetic field, the magnetic flux linked with the coil changes and the current is induced in the coil, its direction being given by Fleming’s right hand rule. Considering the armature to be in vertical position and as it rotates in anticlockwise direction, the wire ab moves upward and cd downward, so that the direction of induced current is shown in fig. In the external circuit, the current flows along B₁R_L B₂.

The direction of current remains unchanged during the first half turn of armature. During the second half revolution, the wire ab moves downward and cd upward, so the direction of current is reversed and in external circuit it flows along B₂R_L B₁. Thus the direction of induced emf and current changes in the external circuit after each half revolution.

Let, N be the number of turns in the coil,

      f is the frequency of rotation,

     A is the area of coil,

     B is the magnetic induction.

Then, the induced emf is given by, 
 
We can see that the emf and current produced is alternating.

Current produced by an ac generator cannot be measured by moving coil ammeter; because the average value of ac over full cycle is zero.

The source of energy generation is the mechanical energy of rotation of armature coil.

OR

Consider a coil of self-inductance L and negligible ohmic resistance. An alternating potential difference is applied across the ends. The magnitude and direction of AC is changing periodically, changing the magnetic flux. So, an emf is induced and produced in the coil. The instantaneous value of alternating voltage applied is given by, 
                                   V = V_o sin w t

Instantaneous induced emf is, 

According to Kirchhoff’s second law in closed circuit, we get

Integrating with respect to time ‘t’,
 

which is the required expression for current.
;
where,  is the peak value of alternating current.

From the above equations we can say that the current lags behind the applied voltage by an angle . 

b)     
i) Induced emf,  = B_HvL ; where B_H is horizontal component of earth’s magnetic field directed from South to North.

ii) West to East

iii) East end of the wire is at higher potential