Question

A 120-V motor has mechanical power output of 2.10 hp. It is 80.0% efficient in convertingpower that it takes in by electrical transmission into mechanicalpower.
(a) Find the current in the motor.
(b) Find the energy delivered to the motor by electricaltransmission in 2.50 h of operation.
(c) If the electric company charges $0.160/kWh, what does it costto run the motor for 2.50 h?

Answer 1

Answer:

a) 16.3 A

b) 17.6 MJ

c) $0.78

Explanation:

The mechanical power is watts is given by:

$P_m=2.10hp*\frac{745.7W}{1hp}=1566W$

The mechanical power is 80% of the electrical power so:

$P_e=\frac{P_m}{0.8}=\frac{1566W}{0.8}=1958W$

The electrical power in the motor is given by:

$P_e=V*I\\where:\\V=voltage\\I=current$

so the current in the motor is:

$I=\frac{P_e}{V}\\\\I=\frac{1958W}{120V}=16.3A$

Watt is equivalent to J/s, so the energy is given by:

$E_m=P_e*t\\E_m=1958W*2.50h*\frac{3600s}{1h}=17.6MJ$

The total cost is given by:

$T_{cost}=0.160\frac{\ }{kW.h}*1.958kW*2.50h=\ 0.78$