A small motor draws a current of 1.76 A from a 110 V line. The output power of the motor is 0.20 hp.
(a) At a rate of $0.060/kWh, what is the cost, in cents, of operating the motor for 4.0 h?
(b) What is the efficiency of the motor?
for (a) i am doing IV*hours*price and its coming up worng.
and for (b) i changed .2hp into Watts. and i got 149.2W.
im just not sure how to do this problem.
Pin=VI=110 * 1.76=193.6W = 0.1936KW.
a. C = $0.060/kwh * 0.1936kw * 4h =
$0.0465 = 4.65 cents.
b. Po = 0.2hp * 746W/hp = 149.2W.
%Eff.=(Po/Pin)100%,
%Eff.=(149.2/193.6)100% = 77.1
To solve this problem, let's break it down into smaller steps:
(a) Cost of operating the motor for 4.0 h:
1. Start by calculating the total energy consumed by the motor. Energy = Power x Time.
In this case, Power = 1.76 A x 110 V = 193.6 W (watts)
Time = 4.0 h (hours)
Energy = 193.6 W x 4.0 h = 774.4 Wh (watt-hours)
2. Convert watt-hours (Wh) to kilowatt-hours (kWh). Divide the energy by 1000.
774.4 Wh ÷ 1000 = 0.7744 kWh
3. Calculate the cost of operating the motor for the given time at the given price.
Cost = Energy (kWh) x Price (per kWh)
Cost = 0.7744 kWh x $0.060/kWh = $0.046464.
Since the question asks for the cost in cents, we need to convert dollars to cents. Multiply the cost in dollars by 100.
Cost = $0.046464 x 100 = 4.6464 cents.
Therefore, the cost of operating the motor for 4.0 h is approximately 4.6464 cents.
(b) Efficiency of the motor:
To calculate the efficiency of the motor, we need to know the input power and the output power.
1. Convert the output power from horsepower (hp) to watts (W).
1 hp is approximately equal to 746 W.
Output power = 0.20 hp x 746 W/hp = 149.2 W
2. Efficiency = (Output Power / Input Power) x 100%
Input Power = Power = 1.76 A x 110 V = 193.6 W
Efficiency = (149.2 W / 193.6 W) x 100% = 77.1%
Therefore, the efficiency of the motor is approximately 77.1%.