An electric furnace runs nine hours a day to heat a house in January (31 days). The heating element has a resistance of 10.6 ohms and is hooked up to a 240 Volt potential. What does it cost to run the furnace in the month of January if the cost of electricity is $0.15 per KW*hr?
***PLEASE SHOW ALL WORK!!!
Power = V^2/R = 5434 Watts
= 5.434 kw
hours = 31*9 = 279 hours
so
5.434 kw * 279 hr *.15/(kw hr)
= $ 227.41
What do I plug in for V and for R?
To calculate the cost of running the furnace for the month of January, we need to determine the power consumed by the furnace and then multiply it by the total number of hours it runs in January and the cost of electricity.
Step 1: Calculate the power consumed by the furnace.
We can use the formula P = V^2 / R, where P is power, V is voltage, and R is resistance.
Plugging in the values, we have P = (240 V)^2 / 10.6 Ω.
P = (240)^2 / 10.6
P = 57600 / 10.6
P ≈ 5433.96 Watts
So, the power consumed by the furnace is approximately 5433.96 Watts or 5.434 KW.
Step 2: Calculate the total energy consumed by the furnace in January.
The energy consumed is given by the formula Energy = Power × Time.
Since the furnace runs for nine hours a day for 31 days in January, the total time is 9 hours per day × 31 days = 279 hours.
Energy = 5.434 KW × 279 hours
Energy ≈ 1515.786 KWh
Step 3: Calculate the cost of electricity.
The cost of electricity is given as $0.15 per KWh.
Cost = Energy × Cost per KWh
Cost = 1515.786 KWh × $0.15
Cost ≈ $227.37
Therefore, it will cost approximately $227.37 to run the electric furnace in the month of January.