Question

The field coils of a 6-pole DC generator each having 500 turns are connected in series. When the field is excited, there is a magnetic flux of 0.02 Wb/pole. If the field circuit is opened in 0.02 s and the residual magnetism is 0.002 Wb/pole, calculate the average voltage induced across the field terminals.

1. 16200 V
2. 18000 V
3. 14300 V
4. 3000 V

Answer 1

Correct Answer - Option 1 : 16200 V

Concept:

Faraday's Laws of Electromagnetic Induction

Faraday summed up the facts of Electromagnetic Induction into two laws. They are

First law:

• Whenever the magnetic field linked with a circuit changes, an EMF is always induced in it. or
• Whenever a conductor cuts a magnetic field EMF is induced in it.
   

Second law:

• The magnitude of induced EMF is equal to the rate of change of flux linkages.

Induced EMF equation:

From both the laws,

Induced EMF (E) = N\({dϕ \over dt}\)

where N = Number of turns of a coil.

dϕ = Change of flux linkages in the coil.

dt= Change in time.

Calculation:

Given

P = Number of poles = 6

N = Total turns = 6 × 500 = 3000  (since 500 turns per pole in series)

Total initial flux = 6 × 0.02 = 0.12 Wb. (since number of poles is 6)

Total residual flux = 6 × 0.002 = 0.012 Wb

Change in flux, dϕ = 0.12 - 0.012 = 0.108 Wb

Time of opening of circuit, dt = 0.02 second

From concept,

Induced EMF (E) = \(3000\times{0.108\over0.02 }\) = 16,200 V