(a) Principle of ac generator
working
Mark labelled diagram
Derivation of the expression for induced emf
(b) Calculation of potential difference
(a) The AC Generator works on the principle of electromagnetic induction.
When the magnetic flux through a coil changes, an emf is induced in it.
As the coil rotates in magnetic field the effective area of the loop, (i.e. A‌cos‌θ) exposed to the magnetic field keeps on changing, hence magnetic flux changes and an emf is induced.
When a coil is rotated with a constant angular speed ' ω ', the angle ' θ ' between the magnetic field vector B and the area vector A , of the coil at any instant ' t ' equals ωt ; (assuming θ=0∘ at t=0 ) As a result, theeffective area of the coil exposed to the magnetic field changes with time; The flux at any instant ' t ' is given by
ϕB=NBA‌cos‌θ=NBA‌cos‌ω‌t
∴ The induced emf e=−N‌

dϕ

dt

‌=−NBA‌

dϕ

dt

(cos‌ω‌t)
e=‌NBAωsin‌ωt
(b) Potential difference developed between the ends of the wings ' e ' =Blv
Given Velocity v=900‌km∕hour
=250m∕ s
Wing span (l)=20m
Vertical component of Earth's magnetic field
Bv‌=BH‌tan‌δ
‌=5×10−4(tan‌30∘)‌ Tesla ‌
∴ Potential difference
‌=5×10−4(tan‌30∘)×20×250
‌=‌

5×20×250×10−4

√3

‌=1.44‌ volt ‌
OR
(a) Identification of the device X Expression for reactance
(b) Graphs of voltage and current with time
(c) Variation of reactance with frequency (Graphical variation)
(d) Phasor Diagram
(a) X : capacitor
Reactance Xc=‌

1

ωC

=‌

1

2πvC

(b)
(c) Reactance of the capacitor varies in inverse proportion to the frequency i.e., Xcα‌

1

v

‌‌