Answer :

To determine the frequency of the voltage generated by a 6-pole generator rotating at 1000 revolutions per minute (rpm), we can use the formula:

[tex]\text{Frequency} = \frac{\text{Number of Poles} \times \text{Speed in RPM}}{120}[/tex]

In this case:

  • Number of poles = 6
  • Speed in RPM = 1000

Substituting these values into the formula gives:

[tex]\text{Frequency} = \frac{6 \times 1000}{120} = \frac{6000}{120} = 50 \text{ Hz}[/tex]

Therefore, the frequency of the generated voltage is 50 hertz (Hz).

Explanation:

  1. Pole Count: The number of poles in a generator affects the frequency of the voltage it produces. More poles mean more cycles of AC voltage in the same time period.

  2. Speed in RPM: RPM (revolutions per minute) indicates how fast the generator is rotating. The faster it spins, the higher the frequency of the generated voltage, assuming the same number of poles.

  3. Formula Derivation: The formula [tex]\text{Frequency} = \frac{\text{Poles} \times \text{RPM}}{120}[/tex] is derived from the relation between rotational speed and electrical cycles. This formula assumes a synchronization between the mechanical rotation and electrical generation in AC (Alternating Current) generators.

This knowledge is often applied in engineering fields related to power systems and machinery design.

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Rewritten by : Barada