To find out how much it costs to operate the router, we can follow these steps:
1. **Calculate the Power Consumption in Watts:** First, we need to calculate the power consumed by the router in watts using Ohm's Law, which relates power (P), voltage (V), and current (I) by the formula:
\[ P = V \times I \]
We're given that the router uses a current (I) of 12 amperes and operates in a 120-volt electrical circuit. Therefore:
\[ P = 120 \, \text{volts} \times 12 \, \text{amperes} \]
\[ P = 1440 \, \text{watts} \]
2. **Convert Power Consumption to Kilowatts:** Power companies typically charge for energy use in kilowatt-hours. There are 1000 watts in a kilowatt, so we must convert the power consumption to kilowatts by dividing by 1000.
\[ P_{\text{kW}} = \frac{P}{1000} \]
\[ P_{\text{kW}} = \frac{1440}{1000} \]
\[ P_{\text{kW}} = 1.44 \, \text{kilowatts} \]
3. **Calculate Energy Consumption in Kilowatt-Hours:** To calculate the energy consumed, we multiply the power consumption in kilowatts by the time (in hours) the router was in use. The time given is 4 hours.
\[ E = P_{\text{kW}} \times \text{Time} \]
\[ E = 1.44 \, \text{kW} \times 4 \, \text{hours} \]
\[ E = 5.76 \, \text{kilowatt-hours} \]
4. **Calculate the Cost of Electricity:** Finally, we calculate the total cost by multiplying the energy consumed in kilowatt-hours by the cost per kilowatt-hour. The cost per kilowatt-hour is given as $0.12.
\[ \text{Cost} = E \times \text{Cost per kWh} \]
\[ \text{Cost} = 5.76 \, \text{kWh} \times \$0.12/\text{kWh} \]
\[ \text{Cost} = \$0.6912 \]
Therefore, it would cost $0.6912 to operate the router for 4 hours. If you need to report this in a standard currency format, it might be common to round to the nearest cent, giving a final answer of $0.69.
