Final answer:
The effective resistance of a 408-V AC, 50.0 kW air conditioner is approximately 3.34 ohms. The cost of running the air conditioner for 8 hours per day over 30 days at 9 cents per kilowatt-hour is $1080.
Step-by-step explanation:
To find the effective resistance of the air conditioner operating on a 408-V AC and consuming 50.0 kW, we use the formula P = V^2 / R, where P is power, V is voltage, and R is resistance. Solving for R gives us R = V^2 / P. Plugging in the given values: R = (408^2) / 50.0 kW, we find that the effective resistance is approximately 3.34 ohms.
To calculate the cost of running the air conditioner during a hot summer month, we multiply the power consumption by the number of hours per day and days in the month, then multiply by the cost of electricity. The formula is Cost = Power (kW) × Time (hours) × Days × Electricity cost (cents/kW·h). Therefore, the cost is 50 kW × 8 h/day × 30 days × $0.09/kW·h, which equals $1080.