Answer this
Dont give any linkss
Q. Derive an expression for the instantaneous value of emf induced in the coil. Why is the emf is maximum when the plane of the armature is parallel to the magnetic field? 

Dear Student ,
 

Please refer tot he following figure

Here,

only the cosine component (which is perpendicular) imparts emf to the rotation coil.

So,

flux linkages of the coil will be

= number of turns in the coil × flux linking

φ = n × φ_maxcoswt

now,

the emf will be

E = -d[φ]/dt

= -d/dt[n × φ_maxcoswt]

thus,

E = n × φ_maxw.sinwt

here maximum value of emf will be [for sinwt = 1]

E_max = n × φ_maxw

thus,

we have

E = E_maxsinwt

or

E = E_maxsinθ

which is the instantaneous value of emf, continuously changing with time or angle.

The emf of a generator is given by the rate of change of magnetic flux passing through the coil. Now when the rate of change of magnetic flux be maximum, there the emf too will be maximum. Let us see mathematically,

Φ = BAcosωt

By Faraday’s law

e = -dΦ/dt

=> E  = BωAsinωt

=> E = E₀sinωt

θ = ωt

=> E = E₀sinθ

Now E will be maximum if θ = π/2 rad.

This means E will be maximum if normal to the plane of coil is perpendicular to the magnetic field. Thus, plane of the coil must lie along the magnetic field.  

Regards