An alternator has 20 poles and running at 300 RPM will generate alternating voltage and current whose frequency is-

Question

Prepp Team · Accepted Answer

Understanding Alternator Frequency Calculation

The question asks us to determine the frequency of the alternating voltage and current generated by an alternator. An alternator produces AC voltage and current based on its number of magnetic poles and its rotational speed. The relationship between these three quantities is fundamental in electrical engineering.

Key Formula for Alternator Frequency

The frequency (f) of the generated voltage in Hertz (Hz) is directly proportional to the number of poles (P) and the speed of rotation (N) in revolutions per minute (RPM). The standard formula connecting these parameters is:

$$f = \frac{P \times N}{120}$$

Where:

f is the frequency in Hertz (Hz)
P is the total number of magnetic poles on the rotor (always an even number)
N is the speed of the rotor in revolutions per minute (RPM)

The constant 120 in the denominator comes from converting RPM to revolutions per second (dividing by 60) and accounting for the fact that one electrical cycle is completed over two pole pitches (multiplying by 2).

Calculating the Frequency for the Given Alternator

We are given the following information for the alternator:

Number of poles, P = 20
Speed of rotation, N = 300 RPM

Now, we can plug these values into the formula to calculate the frequency:

$$f = \frac{P \times N}{120}$$

$$f = \frac{20 \times 300}{120}$$

First, calculate the product of poles and speed:

$$20 \times 300 = 6000$$

Now, divide this result by 120:

$$f = \frac{6000}{120}$$

$$f = 50$$

So, the frequency of the alternating voltage and current generated by the alternator is 50 Hz.

Summary of Calculation

Parameter	Value
Number of Poles (P)	20
Speed (N)	300 RPM
Formula	$$f = \frac{P \times N}{120}$$
Calculation	$$f = \frac{20 \times 300}{120} = \frac{6000}{120} = 50 \text{ Hz}$$

Therefore, the alternator running at 300 RPM with 20 poles will generate voltage and current with a frequency of 50 Hz.

Revision Table: Alternator Frequency

Concept	Description	Formula
Alternator Frequency (f)	Rate at which the alternating voltage/current completes one cycle. Measured in Hertz (Hz).	$$f = \frac{P \times N}{120}$$
Number of Poles (P)	Number of magnetic poles in the alternator rotor. Determines the number of electrical cycles per mechanical revolution. Must be even.
Speed (N)	Rotational speed of the rotor. Measured in revolutions per minute (RPM).

Additional Information: Alternator Fundamentals

Alternators, also known as synchronous generators, are crucial for generating AC power. They work based on Faraday's law of electromagnetic induction.

Principle: Relative motion between a magnetic field and a conductor induces a voltage (EMF) in the conductor.
Components: Typically include a rotor (rotating part, usually the field winding creating the magnetic poles) and a stator (stationary part with armature windings where voltage is induced).
Frequency Standard: Power systems around the world typically operate at standard frequencies, most commonly 50 Hz or 60 Hz. The number of poles and the speed of the alternator are designed or controlled to maintain this standard frequency. For example, to generate 50 Hz, a 2-pole alternator must run at 3000 RPM, a 4-pole at 1500 RPM, and a 20-pole at 300 RPM, as shown in this problem. Similarly, for 60 Hz, a 2-pole runs at 3600 RPM, a 4-pole at 1800 RPM, etc.
Synchronous Speed: The speed at which a synchronous machine (like an alternator or synchronous motor) must rotate to produce or synchronize with a voltage of a specific frequency for a given number of poles. This speed is also given by the formula rearranged for N: $$N = \frac{120f}{P}$$.

Understanding the relationship between poles, speed, and frequency is vital for operating power generation systems and ensuring compatibility with electrical grids.