A. Draw a labeled diagram of AC generator. Derive the expression for the instantaneous value of the emf induced in the coil. B. A circular coil of cross-sectional area and 20 turns is rotated about the vertical diameter with angular speed of in uniform magnetic field of magnitude Calculate the maximum value of the current in the coil. OR A. Draw a labeled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of number of turns and currents in the two coils. B. A power transmission line feeds input power at 2200 V to a step-down transformer with its primary windings having 3000 turns. Find the number of turns in the secondary to get the power output at 220 V.

Question

Philoid · Accepted Answer

A)

The schematic diagram of an AC generator is shown in the above figure. This is an electrical machine which converts mechanical energy into useful electrical energy. AC generator consists of a coil mounted on a rotor shaft. The rotational axis of the coil is kept at 90⁰ to the direction of the magnetic field. The coil (called armature) is mechanically rotated in the uniform magnetic field which can be produced by permanent magnets or electromagnets. The rotation of the coil causes the magnetic flux through it to change, so as per Faraday’s law of electromagnetic induction, an emf is induced in the coil. To connect the coil to the external circuit its ends are connected by slip rings and brushes.

When the coil is rotated with a constant angular speed ω, the angle between the magnetic field vector B and the area vector A of the coil at any instant t is,

Assuming when the coil was at rest, the angle between B and A was zero. As a result, the effective area of the coil exposed to the magnetic field lines changes with time, and thus, the flux at any time t is

By Faraday’s law of electromagnetic induction,

Thus,

e =N B A ω sin ωt

Considering the peak voltage E₀ = B A ω,

e = e₀ sin ωt

If the coil is of N turns the formula becomes,

e = N B A ω sin ωt

And the peak voltage becomes e₀ = N B A ω

B) using the above formula,

e = N B A ω sin ωt

Where given data is,

B = 3.0 × 10^-2 T

A = 200 × 10^-4 m²

ω = 50 rad/s

N = 20 turns, so,

e₀ = N B A ω

E₀ = 3.0 × 10^-2 × 200 × 10^-4 × 50 × 20 = 600000 × 10^-6

E₀ = 0.6 V

Let the resistance of the coil be R, so the peak current in the coil will be,

OR

A) the diagram of a step-up transformer is given below

Transformer uses the principle of mutual induction. A transformer consists of two sets of coils, insulated from each other. They are wound on a soft-iron core, either one on top of the other as shown in the diagram 1 or on separate limbs of the core as shown in the diagram 2. One of the coils called the primary coil has N_P turns. The other coil is called the secondary coil; it has N_S turns.

For a step-up transformer, N_P < N_S

Let the associated flux be , then induced voltage in secondary coil will be

And the back emf generated in the primary coil is,

But we know that, e_p = v_p, so,

So,

Also, in an ideal transformer there is no loss of power so,

i_P v_P = i_S v_S

So,

B) using the above relation on the given data is,

v_P = 2200 V,

N_P = 3000 turns,

v_s = 220 V

we get,

Hence,

N_S = 300 turns.