What is the total cost of using the following at 11¢/kWh? a. 1600 W air conditioner for 6 h b. 1200 W hair dryer for 15 min

Steps to Solve

1. Calculate Energy Consumption for the Air Conditioner

To find the energy consumption, we use the formula for energy in kilowatt-hours (kWh):

$$ \text{Energy (kWh)} = \frac{\text{Wattage (W)} \times \text{Time (hours)}}{1000} $$

Assuming the air conditioner has a wattage of $W_a$ and runs for $T_a$ hours, the energy consumed by the air conditioner is:

$$ E_a = \frac{W_a \times T_a}{1000} $$

2. Calculate Energy Consumption for the Hair Dryer

Similarly, for the hair dryer, we can calculate its energy consumption using the same formula. Let the wattage be $W_h$ and usage time be $T_h$ hours:

$$ E_h = \frac{W_h \times T_h}{1000} $$

3. Calculate Total Energy Consumption

Now we add the energy consumed by both appliances:

$$ E_{\text{total}} = E_a + E_h $$

Replacing values:

$$ E_{\text{total}} = \frac{W_a \times T_a}{1000} + \frac{W_h \times T_h}{1000} $$

4. Calculate Total Cost

Finally, to find the total cost of electricity, we need to multiply the total energy consumed by the cost per kilowatt-hour ($C$):

$$ \text{Total Cost} = E_{\text{total}} \times C $$

Combining everything, we can write:

$$ \text{Total Cost} = \left( \frac{W_a \times T_a}{1000} + \frac{W_h \times T_h}{1000} \right) \times C $$