Question

Five percent increase in supply frequency will change the synchronous speed of motor by

• A. -10 %
• B. +10 %
• C. -5 %
• D. +5 %

Hint:

Because synchronous speed is directly proportional to frequency (\(N_s \propto f\)), any percentage change in supply frequency results in the exact same percentage change in synchronous speed. No calculation is needed.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The synchronous speed of an alternating current (AC) motor is the rotation speed of the magnetic field created by its stator windings.
This speed is determined by the frequency of the AC power supply and the physical design of the motor (number of magnetic poles).
Key Formula or Approach:
The synchronous speed (\(N_s\)) in revolutions per minute (rpm) is given by:
\[ N_s = \frac{120 f}{P} \] Where: - \(f\) is the supply frequency (Hz).
- \(P\) is the number of stator poles per phase.

Step 2: Detailed Explanation:
Let us analyze the relationship between synchronous speed and supply frequency:
1. From the formula:
\[ N_s \propto f \] This shows that synchronous speed is directly proportional to the supply frequency for a motor with a fixed number of poles (\(P\)).
2. Let the initial frequency be \(f_1\) and the initial synchronous speed be \(N_{s1}\).
If the frequency increases by 5%, the new frequency \(f_2\) is:
\[ f_2 = f_1 \times (1 + 0.05) = 1.05 f_1 \] 3. The new synchronous speed \(N_{s2}\) is:
\[ N_{s2} = \frac{120 f_2}{P} = \frac{120 (1.05 f_1)}{P} = 1.05 \left( \frac{120 f_1}{P} \right) = 1.05 N_{s1} \] 4. Calculate the percentage change in synchronous speed:
\[ \text{Percentage Change} = \frac{N_{s2} - N_{s1}}{N_{s1}} \times 100% = \frac{1.05 N_{s1} - N_{s1}}{N_{s1}} \times 100% = 0.05 \times 100% = +5% \] An increase of 5% in the supply frequency results in exactly a 5% increase in the synchronous speed.

Step 3: Final Answer:
The correct option is (D).