Sure! Let’s go through the detailed, step-by-step solution to determine the rotor speed of the motor.
### Step 1: Identify the given parameters
We are given the following parameters:
- Frequency (f) = 60 Hz
- Number of poles (P) = 6
- Slip (s) = 5% (or 0.05 in decimal form)
### Step 2: Calculate the synchronous speed (Ns)
The synchronous speed of an induction motor can be calculated using the formula:
[tex]\[ N_s = \frac{120 \times f}{P} \][/tex]
Where:
- [tex]\( N_s \)[/tex] = Synchronous speed in revolutions per minute (RPM)
- [tex]\( f \)[/tex] = Frequency in Hertz (Hz)
- [tex]\( P \)[/tex] = Number of poles
Plugging in the given values:
[tex]\[ N_s = \frac{120 \times 60}{6} \][/tex]
[tex]\[ N_s = \frac{7200}{6} \][/tex]
[tex]\[ N_s = 1200 \, RPM \][/tex]
So, the synchronous speed [tex]\( N_s \)[/tex] is 1200 RPM.
### Step 3: Calculate the rotor speed (Nr)
The rotor speed of an induction motor can be calculated using the formula:
[tex]\[ N_r = N_s \times (1 - s) \][/tex]
Where:
- [tex]\( N_r \)[/tex] = Rotor speed in RPM
- [tex]\( N_s \)[/tex] = Synchronous speed in RPM
- [tex]\( s \)[/tex] = Slip (in decimal form)
Substituting the known values:
[tex]\[ N_r = 1200 \times (1 - 0.05) \][/tex]
[tex]\[ N_r = 1200 \times 0.95 \][/tex]
[tex]\[ N_r = 1140 \, RPM \][/tex]
So, the rotor speed [tex]\( N_r \)[/tex] is 1140 RPM.
### Summary
- The synchronous speed [tex]\( N_s \)[/tex] of the motor is 1200 RPM.
- The rotor speed [tex]\( N_r \)[/tex] of the motor is 1140 RPM.
Thus, the rotor speed of the six-pole, 60 Hz motor with 5% slip is 1140 RPM.
