Electric Motor Efficiency: Calculating Current, Energy, and Cost
What are the values needed to determine the current, energy, and cost of running an electric motor?
To determine the current, energy, and cost of running an electric motor, we need to know the mechanical power output of the motor, the voltage source it is connected to, and the efficiency of the motor in converting electrical power to mechanical power.
Calculating Current, Energy, and Cost
The mechanical power output of an electric motor is 3.30 hp, which is approximately 2,460 W. The motor is connected to a 120 V source and is 94.0% efficient in converting power.
To calculate the current delivered to the motor, we first need to determine the input power of the motor. The input power (P) can be found using the formula P = IV, where I is the current. Since the motor is 94% efficient, the input power is 2,460 W / 0.94 = 2,617 W. Therefore, the current delivered to the motor is 2,617 W / 120 V = 21.81 A.
Next, we calculate the energy delivered to the motor by multiplying the power by the time of operation. The energy delivered is 2,617 W * 3.80 h = 9.95 MJ.
Finally, to determine the cost of running the motor for 3.80 hours, we need to calculate the energy consumed in kWh and multiply it by the cost per kWh. The energy consumed is 2,617 W * 3.80 h / 1000 = 9.94 kWh. Therefore, the cost to run the motor is 9.94 kWh * $0.110/kWh = $1.09.