At its normal operating speed, an electric fan motor draws only 10.9% of the current it draws when it just begins to turn the fan blade. The fan is plugged into a 120.0-V socket. What back emf does the motor generate at its normal operating speed?
To find the back emf generated by the motor at its normal operating speed, we need to use the given information about the current at different speeds.
The back emf (Eb) generated by an electric motor can be calculated using the formula:
Eb = V - I * R
Where:
- Eb is the back emf
- V is the voltage supplied to the motor
- I is the current drawn by the motor
- R is the resistance of the motor
In this case, the voltage supplied to the motor (V) is 120.0V.
The problem states that the current drawn by the motor at its normal operating speed is only 10.9% of the current when it just begins to turn the fan blade.
Let's assume the current when it just begins to turn the fan blade is I_initial and the current at normal operating speed is I_normal.
So we have:
I_normal = 0.109 * I_initial
We can rewrite this equation as follows:
I_initial = I_normal / 0.109
Now we need to find the value of I_initial.
To do that, we can use the relationship between voltage (V), current (I), and power (P):
P = V * I
The power consumed by the motor is the same when it just begins to turn the fan blade and at its normal operating speed. Therefore, we can write:
V * I_initial = V * I_normal
Since we know V and I_normal from the given information, we can substitute those values into the equation above and solve for I_initial.
Once we have the value of I_initial, we can calculate the back emf (Eb) using the formula mentioned earlier:
Eb = V - I_initial * R
Note: To find the value of resistance (R), additional information about the motor or its specifications is required.