Final answer:
To calculate the cost of running an electric furnace during January, multiply the power consumed by the time it runs and the cost per kWh of electricity. The total cost for running the furnace throughout January is $87.43.
Step-by-step explanation:
Calculating the Cost of Running an Electric Furnace
To find the cost of running the furnace during January, we need to calculate the energy consumed by the furnace and then multiply by the cost of electricity. The furnace runs for 10 hours a day for 31 days. The heating element has a resistance of 5.1 Ω (ohms) and the current it carries is 23.5 A (amperes).
The power (P) consumed by the furnace can be found using the formula P = I2R, where I is the current and R is the resistance. Thus, P = (23.5 A)2 × 5.1 Ω = 2820.375 W, which is 2.820375 kW. Over January, the furnace runs for 10 hours a day for 31 days, resulting in a total time of 310 hours.
The total energy consumed (E) in kilowatt-hours (kWh) is the product of power in kilowatts (kW) and time in hours (h). So, E = 2.820375 kW × 310 h = 874.31625 kWh. With an electricity cost of $0.10/kWh, the cost (C) for January is C = 874.31625 kWh × $0.10/kWh = $87.43.
Therefore, the cost of running the electric furnace for January is $87.43.