Professional Analysis of Electrical Motor Efficiency

What are the calculations needed to determine the current, energy consumption, and cost of running a 120-V motor with a mechanical power output of 2.10 hp and 80.0% efficiency?

a) What is the current flowing through the motor?

b) How much energy is delivered to the motor in 2.50 hours of operation?

c) How much does it cost to run the motor for 2.50 hours if the electric company charges $0.160/kWh?

Answers:

a) 16.3 A

b) 17.6 MJ

c) $0.78

In order to analyze the efficiency and cost of running a 120-V motor with a mechanical power output of 2.10 hp, we need to consider the electrical power, current, energy consumption, and overall cost.

Calculation for Current:

The mechanical power output of the motor is 2.10 hp, which is equivalent to 1566 watts (W). Since the motor is 80% efficient, the electrical power input is 1958 W. To find the current flowing through the motor, we use the formula:

Current (I) = Electrical Power (P_e) / Voltage (V)

Therefore, I = 1958 W / 120 V = 16.3 A.

Calculation for Energy Consumption:

The energy consumed by the motor in 2.50 hours of operation can be calculated by multiplying the electrical power and time:

Energy (E_m) = Electrical Power (P_e) * Time (t)

E_m = 1958 W * 2.50 h * 3600 s/h = 17.6 MJ.

Calculation for Cost:

If the electric company charges $0.160/kWh, the total cost to run the motor for 2.50 hours is:

Total Cost = Cost per kWh * Electrical Power * Time

Total Cost = $0.160/kWh * 1.958 kW * 2.50 h = $0.78.

By analyzing these calculations, we can determine the current flowing through the motor, the energy consumption during operation, and the cost of running the motor efficiently.