Question

A small office-building air conditioner operates on 408-V AC and consumes 50.0 kW. (a) What is its effective resistance? (b) What is the cost of running the air conditioner during a hot summer month when it is on 8.00 h per day for 30 days and electricity costs 9.00 cents/kW⋅h?

a) 209 Ω, $108.00
b) 304 Ω, $108.00
c) 209 Ω, $1080.00
d) 304 Ω, $1080.00

Answer 1

The effective resistance of the air conditioner is 66.97 Ω. The cost of running the air conditioner for a month is $1080.

Step-by-step explanation:

(a) To find the effective resistance, we can use Ohm's Law, which states that voltage is equal to the current multiplied by the resistance (V = IR). Since we are given the voltage (408 V) and power (50.0 kW), we can rearrange the formula to solve for resistance. Using the formula: resistance = voltage^2 / power, we can calculate:

resistance = (408 V)^2 / 50.0 kW = 3348.48 V^2 / 50.0 kW = 66.97 Ω

(b) To calculate the cost of running the air conditioner, we can multiply the power (50.0 kW) by the number of hours per month (8.00 h/day * 30 days) and by the cost per kilowatt-hour (9.00 cents/kW.h). Converting cents to dollars, we have:

cost = 50.0 kW * 8.00 h/day * 30 days * 0.09 dollars/kW.h = 1080 dollars