Alternator Frequency Calculation

To determine the frequency of an alternator, we use a fundamental formula that relates the number of poles and the rotational speed of the machine. This calculation is crucial for understanding how electrical power is generated and ensuring it meets the required standards, such as 50 Hz or 60 Hz, for a given power system.

Frequency Relationship in Alternators

The frequency (\(f\)) of the voltage generated by an alternator is directly proportional to the number of poles (\(P\)) and the speed (\(N\)) at which the rotor rotates. The standard formula used for this calculation is:

\(f = \frac{P \times N}{120}\)

Where:

• \(f\) is the frequency in Hertz (Hz).
• \(P\) is the total number of poles (always an even number).
• \(N\) is the rotational speed of the alternator in revolutions per minute (RPM).
• The constant 120 is derived from 2 (for pole pairs) multiplied by 60 (to convert minutes to seconds).

Let's consider the given values in the problem to find the frequency.

Calculating Alternator Frequency Step-by-Step

We are provided with the following information for the alternator:

• Number of poles (\(P\)) = 6
• Rotational speed (\(N\)) = 1500 RPM

Now, we will substitute these values into the frequency formula:

\(f = \frac{P \times N}{120}\)

Substitute \(P=6\) and \(N=1500\):

\(f = \frac{6 \times 1500}{120}\)

First, perform the multiplication in the numerator:

\(6 \times 1500 = 9000\)

Next, divide the result by 120:

\(f = \frac{9000}{120}\)

\(f = 75\)

Therefore, the frequency of the 6-pole alternator running at 1500 RPM is 75 Hz.

Alternator Parameters Summary

Here is a summary of the input parameters and the calculated output frequency:

This calculation clearly shows how the design and operating speed of an alternator determine the output frequency, which is a key characteristic of the generated AC power.