A 120-V motor has mechanical power output of 2.20 hp. It is 92.0% efficient in converting power that it takes in by electrical transmission into mechanical power.
(a) Find the current in the motor.
Po = 2.20hp * 746w./hp = 1641.2 Watts
Pi = Po/0.92 = 1641.2/0.92 = 1784 Watts
Pi = 120*I = 1784 W.
I = 1784/120 = 14.9A.
To find the current in the motor, we need to apply the power equation and the efficiency equation.
First, let's convert the mechanical power output from horsepower (hp) to watts (W), as most electrical calculations use watt as the standard unit of power. To convert from hp to W, we can use the conversion factor: 1 hp = 746 W.
Given that the mechanical power output is 2.20 hp, we can convert it to W:
2.20 hp × 746 W/hp = 1643.2 W
Now, let's use the power equation:
Power = Voltage × Current
We can rearrange the equation to solve for the current:
Current = Power / Voltage
Since the mechanical power output is the mechanical power input (assuming the motor is 100% efficient), we can use it to calculate the current.
Current = 1643.2 W / 120 V
Current ≈ 13.69 A
Therefore, the current in the motor is approximately 13.69 Amperes (A).