Question

Consider a TV set that consumes \(120 \mathrm{W}\) of electric power when it is on and is kept on for an average of 6 hours per day. For a unit electricity cost of 12 cents per \(\mathrm{kWh}\), determine the cost of electricity this TV consumes per month \((30\) days)

Short answer

Question: Determine the cost of electricity consumed by a TV with a power consumption of 120 watts, kept on for an average of 6 hours daily, with an electricity cost of 12 cents per kWh, for a month with 30 days. Answer: The TV consumes \$2.59 worth of electricity in a month (30 days).

Step-by-step solution

Calculate the energy consumed per day

To find the energy consumed by the TV in one day, we can use the formula: Energy = Power x Time. Given Power = 120 W and Time = 6 hrs, we can calculate the energy consumed per day: Energy_per_day (E_day) = 120 W × 6 hrs

Convert watts to kilowatts

We need to convert the power from watts to kilowatts, since the cost is given in cents per kWh: Power_kW = 120 W × \frac{1 \mathrm{kW}}{1000 \mathrm{W}} = 0.12 \mathrm{kW}

Calculate the energy consumed in kilowatt-hours per day

Now, we can calculate the energy consumed per day in kilowatt-hours: Energy_per_day_kWh (E_day_kWh) = 0.12 \mathrm{kW} × 6 \mathrm{hrs} = 0.72 \mathrm{kWh}

Calculate the energy consumed per month

To find the total energy consumed in a month (30 days), we can multiply the daily consumption by 30: Energy_per_month_kWh (E_month_kWh) = 0.72 \mathrm{kWh} × 30\:\mathrm{days} = 21.6 \mathrm{kWh}

Calculate the cost of electricity per month

Finally, using the electricity cost of 12 cents per kWh, we can calculate the total cost of electricity consumed by the TV per month: Cost_per_month = 21.6 \mathrm{kWh} × \$0.12 \mathrm{per\: kWh} = \$2.592 Thus, the TV consumes \$2.59 worth of electricity (rounded to the nearest cent) in a month (30 days).