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

Answer:

a) $i = 15.033\,A$, b) $\dot E_{in} = 1.804\,kW$, c) $C = 0.496\,USD$

Explanation:

a) Electric power transmitted into the motor is:

$\dot E _{in} = \frac{(2.20\,hp)\cdot \left(0.746\,\frac{kW}{hp} \right)}{0.91}$

$\dot E_{in} = 1.804\,kW$

The current in the motor is:

$i = \frac{1804\,W}{120\,V}$

$i = 15.033\,A$

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:

$C = (1.804\,kW)\cdot (2.5\,h)\cdot \left(3600\,\frac{s}{h} \right)\cdot \left(\frac{1}{3600}\,\frac{kWh}{kJ} \right)\cdot \left(0.110\,\frac{USD}{kWh} \right)$

$C = 0.496\,USD$