a window air conditioner is estimated to have a cost of operation of $50 per 30 days. this is based on the assumption that the air conditioner will run half of the time and that electricity costs $.090 per kWh. determine how much current the air conditioner will take from a 120-V outlet
To determine the current the air conditioner will take from a 120V outlet, we can use the formula:
Current (in amperes) = Power (in watts) / Voltage (in volts)
First, let's calculate the power consumed by the air conditioner:
Power = Cost / Time
In this case, the cost of operation is $50 per 30 days, which means the air conditioner consumes $50 worth of electricity in 30 days.
Power = $50 / 30 days
Now, we need to convert the power consumed to watts. Since the power consumption is given in terms of cost and time, we need to use the cost of electricity per kWh.
1 kWh = 1000 watts
The electricity cost is $0.090 per kWh, so we can calculate the power in watts as follows:
Power (in watts) = Power (in kWh) * Conversion factor
Power (in kWh) = Cost / (Electricity cost per kWh)
Power (in watts) = ($50 / 30 days) * (1000 watts / 1 kWh) * ($0.090 / 1 kWh)
Next, we can substitute the power value into the current formula:
Current (in amperes) = Power (in watts) / Voltage (in volts)
Current (in amperes) = (Power (in watts)) / 120 V
Substitute the calculated power value:
Current (in amperes) = (Power (in watts)) / 120 V
Perform the calculations to find the current drawn by the air conditioner from a 120V outlet.
To determine the current drawn by the air conditioner, we can use the formula:
Current (I) = Power (P) / Voltage (V)
First, we need to calculate the power consumption of the air conditioner. Given that the estimated cost of operation is $50 per 30 days, we can find the daily cost by dividing it by 30:
Daily cost = $50 / 30 = $1.67
We know that the air conditioner is estimated to run for half of the time, so the daily usage cost is:
Usage cost per day = $1.67 / 2 = $0.835
Now, we can determine the power consumption using the formula:
Power (P) = Cost / Cost per kWh
Given that electricity costs $0.090 per kWh:
Power (P) = $0.835 / $0.090 = 9.278 kWh
Lastly, we can calculate the current drawn by the air conditioner using the formula mentioned earlier:
Current (I) = Power (P) / Voltage (V)
Voltage (V) = 120 V
Current (I) = 9.278 kWh / 120 V = 0.07732 A
Therefore, the air conditioner will draw approximately 0.07732 Amperes from a 120-V outlet.