How much will it cost you (in cents) to operate a 29 Ω electric skillet on a standard 120 V outlet for 5 hours and 36 minutes? The unit price for electrical energy in this case is 7.350 cents/kWh.
P = E^2/R = 120^2/29 = 497 Watts = 0.497 kW.
Cost = 0.497 * 5.6 * 7.35cents/kWh.
To calculate the cost of operating a 29 Ω electric skillet for 5 hours and 36 minutes, we need to follow these steps:
Step 1: Convert the time duration to hours.
5 hours and 36 minutes can be converted to hours by dividing the minutes by 60 and adding it to the number of hours.
5 hours and 36 minutes = 5 + (36/60) = 5.6 hours
Step 2: Calculate the total energy consumed in kilowatt-hours (kWh).
To calculate the energy consumed, we need to use the formula:
Energy (kWh) = Power (kW) x Time (hours)
The electric skillet's power can be calculated using Ohm's law:
Power (kW) = (Voltage²) / Resistance
Given:
Voltage (V) = 120 V
Resistance (Ω) = 29 Ω
Time (hours) = 5.6 hours
First, we calculate the power:
Power (kW) = (120²) / 29
Power (kW) = 4800 / 29
Power (kW) ≈ 165.52 kW
Next, we calculate the energy consumed:
Energy (kWh) = Power (kW) x Time (hours)
Energy (kWh) = 165.52 kW x 5.6 hours
Energy (kWh) ≈ 925.4912 kWh
Step 3: Calculate the cost of energy consumed.
To find the cost, we multiply the energy consumed by the unit price for electrical energy:
Cost = Energy (kWh) x Unit Price
Cost = 925.4912 kWh x 7.35 cents/kWh
Cost ≈ 6801.23 cents
Therefore, it will cost approximately 6801.23 cents to operate the 29 Ω electric skillet on a standard 120 V outlet for 5 hours and 36 minutes.