(a) State the principle of an ac generator and explain its working with the help of a labelled diagram. Obtain the expression for the emf induced in a coil having N turns each of cross-sectional area A, rotating with a constant angular speed ω in a magnetic field B directed perpendicular to the axis of rotation.
(b) An aeroplane is flying horizontally from west to east with a velocity of 900 km/hour. Calculate the potential difference developed between the ends of its wings having a span of 20 m. The horizontal component of the Earth’s magnetic field is 5 × 10–4 T and the angle of dip is 30° .
OR
A device X is connected across an ac source of voltage V = V0 sin ωt. The current through X is given as
(a) Identify the device X and write the expression for its reactance.
(b) Draw graphs showing variation of voltage and current with time over one cycle of ac, for X.
(c) How does the reactance of the device X vary with frequency of the ac ? Show this variation graphically.
(d) Draw the phasor diagram for the device X.
a) Diagram of ac generator is given below.
Working principle: The working of an ac generator is based on the principle of electromagnetic induction. When a closed coil is rotated in a uniform magnetic field with its axis perpendicular to the magnetic field, the magnetic flux linked with the coil changes and an induced emf and hence a current is set up in it.
Expression for induced emf:
Let N = number of turns in the coil
A = face area of each turn
B = magnitude of the magnetic field
θ = angle which normal to the coil makes with filed B
ω = the angular frequency with which coil rotates
Then the magnetic flux linked with coil at any instant t will be
∅ = NBA cosθ = NBA cos ωt
By faraday’s flux rule, the induced emf is given by
ϵ = ϵo sinωt
where ϵo = NBAω
b) Potential difference developed between the ends of the wings e = Bl