What would be the frequency if the speed of rotation is doubled and the number of poles remains the same?

The frequency in an electrical system is directly related to the speed of rotation and the number of poles. Specifically, the formula for frequency (f) is given by:

[ f = \frac{P \cdot n}{120} ]

where ( P ) is the number of poles and ( n ) is the speed of rotation in revolutions per minute (RPM).

When the speed of rotation is doubled while keeping the number of poles constant, this formula indicates that the frequency will also double. This is because frequency is proportional to the speed of rotation; if the speed increases, the cycles produced per unit time increase as well, thus doubling the frequency.

In this case, since the number of poles does not change, the only factor affecting frequency is the change in the speed of rotation. Therefore, if the speed is doubled, the frequency must also double.

This relationship is foundational in understanding motor theory and electrical generation principles, particularly in alternating current (AC) systems. Understanding this principle helps in the design and analysis of electrical systems and machines.