Question

A 120-V motor has mechanical power output of 2.20 hp. It is 91.0% efficient in converting power that it takes in by electrical transmission into mechanical power. (a) Find the current in the motor. A (b) Find the energy delivered to the motor by electrical transmission in 2.50 h of operation. MJ (c) If the electric company charges $0.110/kWh, what does it cost to run the motor for 2.50 h

Answer 1

a)
`i = 15.033\,A`, b)
`\dot E_(in) = 1.804\,kW`, c)
`C = 0.496\,USD`

Step-by-step explanation:

a) Electric power transmitted into the motor is:

`\dot E _(in) = ((2.20\,hp)\cdot \left(0.746\,(kW)/(hp) \right))/(0.91)`

`\dot E_(in) = 1.804\,kW`

The current in the motor is:

`i = (1804\,W)/(120\,V)`

`i = 15.033\,A`

b) The energy delivered to the motor is:

`\dot E_(in) = 1.804\,kW`

c) The cost of running the motor for 2.50 hours is:

`C = (1.804\,kW)\cdot (2.5\,h)\cdot \left(3600\,(s)/(h) \right)\cdot \left((1)/(3600)\,(kWh)/(kJ) \right)\cdot \left(0.110\,(USD)/(kWh) \right)`

`C = 0.496\,USD`