# Consider a coil rotating at a speed of N rpm in the field of P poles. As the coil moves past successive north the south poles, one complete cycle is generated. What is the frequency of the generated voltage?

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SSC JE EE Previous Paper 10 (Held on: 10 Dec 2020)
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1. $$\frac{{PN}}{{60}}$$
2. $$\frac{{PN}}{{120}}$$
3. $$\frac{{120\;P}}{N}$$
4. $$\frac{{120\;f}}{P}$$

## Answer (Detailed Solution Below)

Option 2 : $$\frac{{PN}}{{120}}$$
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CT 1: Basic Concepts
18600
10 Questions 10 Marks 6 Mins

## Detailed Solution

Expression for frequency in a Generator:

• 3-phase supply with a frequency of ‘f’ is given to the 3-phase distributed winding the rotating magnetic field is set up by the windings.
•  The speed of the rotating magnetic field is in synchronous with supply frequency and hence called synchronous speed ‘N’ (in rpm).
• 3-phase windings are wound for specific even number of poles ‘P’, 2/4/6/8…
• One cycle of AC current through the windings make the pole axes to move along one pair of poles (P/2).
• Hence fs cycle per second AC current will give rise the speed of rotating magnetic field as :

$$\frac{N}{{60}} = \frac{f}{{\frac{{\rm{P}}}{2}}}$$ rps.

• Rearrangement of the above equation will give the equation for synchronous speed in rpm as:

$$N = \frac{{120 \times {\rm{f}}}}{{\rm{P}}}$$ rpm.

• Frequency is expressed as $$\frac{{NP}}{{120}}$$ Hertz.