Question

A 120-V motor has mechanical power output of 2.50hp. It is 90.0% efficient in converting power that it takes in by electrical transmission into mechanical power. (b) Find the energy delivered to the motor by electrical transmission in 3.00 \mathrm{~h} of operation.

Answer 1

1. The current in this motor is equal to 17.27 Ampere.
2. The energy delivered to this motor in 3.00 hours is equal to 22.38 Megajoules.
3. At $0.110/kWh, the cost to run the motor for 3.00 hours is equal to $0.684.

How to determine the current (in A) delivered to the motor?

Assuming this electric motor is a single-phase motor and it operates by using DC current, its mechanical power output would be given by:

W = ηIV

Making current (I) the subject of formula, we have:

I = ηV/W

Substituting the given parameters into the formula, we have;

I = (2.50 × 0.746 × 1000)/(0.9 × 120)

I = 1,865/108

Current, I = 17.27 Ampere.

For the energy delivered to this motor, we have:

First of all, we would determine the power delivered to this motor as follows:

Power, P = IV

Power, P = 17.27 × 120

Power, P = 2,072.4 Watt.

Therefore, the energy delivered to this motor in 3.00 hours is given by:

Energy = power × time

Energy = 2,072.4 × 3.00 × 3,600 × 1/1000000

Energy = 22.38 Megajoules.

How to determine the cost?

At $0.110/kWh, the cost to run the motor for 3.00 hours is given by:

Cost = 0.110 × 22.38 × 0.278

Cost = $0.684.

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Complete Question:

A 120-V motor has mechanical power output of 2.50 hp. It is 90.0% efficient in converting power that it takes in by electrical transmission into mechanical power.

(a) Find the current in the motor.

(b) Find the energy delivered to the motor by electrical transmission in 3.00 h of operation.

(c) If the electric company charges $0.110/kWh, what does it cost to run the motor for 3.00 h?