An electric space heater draws 15.5 A from a 120 V source. It is operated, on the average, for 4.0 h each day.
(b) How much energy in kWh does in consume in 30 days?
(c) At 11 per kWh, how much does it cost to operate the heater for 30 days?
15.5A * 120V * 1W/VA* 4h/day * 1kWh/1000Wh * 30day = 223.2 kWh
now multiply by rate to get cost
To answer part (b), we need to calculate the energy consumed by the space heater over a period of 30 days. The formula for calculating energy consumption is:
Energy (kWh) = Power (kW) x Time (hours)
To find the power consumption in kilowatts (kW), we need to convert the current from amperes (A) to kilowatts using Ohm's Law. The formula is:
Power (kW) = Current (A) x Voltage (V) / 1000
Substituting the given values:
Current = 15.5 A
Voltage = 120 V
Power (kW) = 15.5 A x 120 V / 1000 = 1.86 kW (rounded to two decimal places)
Now, we can calculate the energy consumption in kWh over 30 days:
Time (hours) = 4.0 h x 30 days = 120 hours
Energy (kWh) = 1.86 kW x 120 hours = 223.2 kWh (rounded to one decimal place)
Therefore, the space heater consumes 223.2 kWh of energy in 30 days.
To answer part (c), we need to calculate the cost of operating the heater for 30 days. Given that the cost per kWh is $0.11:
Cost = Energy (kWh) x Cost per kWh
Substituting the values:
Energy (kWh) = 223.2 kWh
Cost per kWh = $0.11
Cost = 223.2 kWh x $0.11 = $24.55 (rounded to two decimal places)
Therefore, it costs $24.55 to operate the heater for 30 days at a rate of $0.11 per kWh.
To find the energy consumed by the space heater in kWh, we need to calculate the power consumed in watts and then convert it to kilowatts.
(a) The power consumed by the space heater can be calculated using the formula:
Power (P) = Voltage (V) * Current (I)
Given that the voltage (V) is 120 V and the current (I) is 15.5 A, we can substitute these values into the formula:
P = 120 V * 15.5 A
P = 1860 W
Now, we can convert this power to kilowatts (kW):
P (kW) = P (W) / 1000
P (kW) = 1860 W / 1000
P (kW) = 1.860 kW
(b) To find the energy consumption in kWh for 30 days, we can use the formula:
Energy (kWh) = Power (kW) * Time (hours)
Given that the time is 4.0 hours per day and we are calculating for 30 days, we can substitute these values into the formula:
Energy (kWh) = 1.860 kW * 4.0 h/day * 30 days
Energy (kWh) = 223.2 kWh
Therefore, the space heater consumes 223.2 kWh in 30 days.
(c) To find the cost of operating the heater for 30 days at the rate of $0.11 per kWh, we can multiply the energy consumption by the cost per kWh:
Cost = Energy (kWh) * Cost per kWh
Cost = 223.2 kWh * $0.11/kWh
Cost = $24.52
Therefore, it would cost $24.52 to operate the heater for 30 days at the rate of $0.11 per kWh.