(a) What is the current in the motor?
(b) How much energy is delivered to the motor by electrical transmission in 2.70 hours of operation?
(c) If the price of electricity is $0.110/kWh, what does it cost to operate this motor for 2.70 hours ?
(a) The current in the motor is 105.72 amperes.
(b) 5714.526 watt-hours energy is delivered to the motor by electrical transmission in 2.70 hours.
(c) $0.62859786 is the cost to operate this motor for 2.70 hours.
Calculating Current in the Motor:
To find the current in the motor, we can use the formula: Power (P) = Voltage (V) × Current (I). Given that the motor is connected to a 20-V power supply and has a power output of 2.70 hp, we first need to convert horsepower to watts. 1 hp is equivalent to 746 watts, so the motor's power output is 2.70 × 746 = 2014.2 watts. Since the motor is 95.0% efficient, we can calculate the power input by dividing the power output by the efficiency: Power input = Power output / Efficiency. Therefore, the power input is 2014.2 / 0.95 = 2114.42 watts. Now we can find the current by rearranging the formula: I = P / V. Substituting the values, we get I = 2114.42 / 20 = 105.72 amperes.
Calculating Energy Delivered to the Motor:
To determine the energy delivered to the motor by electrical transmission in 2.70 hours of operation, we can use the formula: Energy (E) = Power (P) × Time (t). Given that the power input is 2114.42 watts and the time of operation is 2.70 hours, we can calculate the energy delivered by multiplying these values: E = 2114.42 × 2.70 = 5714.526 watt-hours.
Calculating Cost of Operating the Motor:
To find the cost of operating the motor for 2.70 hours, we need to calculate the total energy consumed and then multiply it by the price of electricity per kilowatt-hour. Since 1 kilowatt-hour is equal to 1000 watt-hours, we divide the energy consumed by 1000 to convert it to kilowatt-hours: Energy consumed = 5714.526 / 1000 = 5.714526 kilowatt-hours. Multiplying the energy consumed by the price per kilowatt-hour, which is $0.110, gives us the cost of operating the motor: Cost = Energy consumed × Price per kilowatt-hour = 5.714526 × $0.110 = $0.62859786.