A 120-V motor has mechanical power output of 3.00 hp. It is 83.0% efficient in c

Question

A 120-V motor has mechanical power output of 3.00 hp. It is 83.0% 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 2.00 h of operation. c)If the electric company charges $0.160/kWh, what does itcost to run the motor for 2.00h ? A 120-V motor has mechanical power output of 3.00 hp. It is 83.0% 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 2.00 h of operation. c)If the electric company charges $0.160/kWh, what does itcost to run the motor for 2.00h ?

Explanation / Answer

Voltage V = 120 V

Mechanical Power P = 3 hp = 3 * 746 W = 2238 W

Effciency e = 83 % = 0.83

So, electrical power P ‘ = P / 0.83 = 2696.38 W

(a). current I = P ‘ / V = 22.46 A

(b). time t= 2 h = 2 * 3600 s

Energy delivered to the motor E = P ‘ t

                                                    = 19.41 * 10 ^ 6 J

(c). energy E = 19.41 * 10 ^ 6 J

                     =19.41 * 10^ 6 W s

                    = 19.41 * 10 ^ 6 * ( kW / 10 ^ 3 ) * ( 1/ 3600) h

                    =5.391 kW h

Cost of 1 kW h is , C = $0.16

So, Cost of 5.391 kWh is = 5.391 * $0.16

                                         = $0.86266

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