An electric motor operating at steady state draws a current of 20 amp at a voltage of 110 v. the output shaft rotates at a constant speed of 2000 rpm and exerts a torque of 9.07 n middot m. determine the input power, in w. the output power, in w. the cost of 24 hours of operation if electricity is valued at $0.09 per kw middot h.

Input power = 2200 w

Output power = 1899.7 w

Cost = $ 4.752

Explanation:

Assuming a Direct Current scenario, electric input power is calculated by:

Where  

Pi is Power in watts (w)

V is voltage in volts (v)

I is current in amperes (a)

Then, the formula for output power is

Where  

Po is Power in watts (w)

T is torque in NM (v)

S is speed in RPM (rpm)

9.5488 is used to convert rpm unit to rad/sec unit

Finally, to calculate the cost of operation, we simply multiply the input power, total hours of operation and value per hour:

Where  

CO is cost of operation in $

Pi is Power in watts (w)

H is operation time in hours (hs)

C is value per kw per hour (kwh)

1000 is used to convert watts unit to kilowatts unit

$

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