Question

(d) optional for g2 science
emily replaces four of the light bulbs in her house with led light bulbs. she keeps
the led light bulbs switched on for 10 hours a day.
(i) calculate the amount of electrical energy consumed by an led light bulb in
kwh, for one day.
amount of electrical energy consumed =
(ii) calculate the amount of electrical energy consumed by an led light bulb in
for one day.
amount of electrical energy consumed =
(iii) the electricity tariff is 15 cents per kwh.
calculate the monthly cost of electrical energy consumption of all four led
light bulbs. assume that there are 30 days in a month. leave your answer in
dollars.

Explanation:

Step1: Identify Missing Information

The problem about calculating electrical energy consumption of LED bulbs is missing the power rating (in watts or kilowatts) of the LED light bulbs. Without this value, we can't perform the energy calculation using the formula \( E = P \times t \) (where \( E \) is energy in kWh, \( P \) is power in kW, and \( t \) is time in hours). For example, if a bulb has a power of \( P \) watts, we first convert it to kilowatts (\( \frac{P}{1000} \) kW) and then multiply by the time (10 hours for part (i) and (ii), and then scale for 30 days and 4 bulbs for part (iii)).

Step2: State the Required Formula and Variables

The formula for electrical energy consumption is \( E = P \times t \), where:

• \( E \): Energy in kilowatt - hours (kWh)
• \( P \): Power of the bulb in kilowatts (kW)
• \( t \): Time in hours (h)

For part (i), if we assume the power of one LED bulb is \( P \) kW, then for one day (10 hours), the energy for one bulb is \( E_1=P\times10 \) kWh. For four bulbs, it would be \( E_{4}=4\times P\times10 = 40P \) kWh.

For part (ii), if we want the energy in joules, we know that \( 1\space kWh = 3.6\times 10^{6}\space J \), so we can convert the kWh value from part (i) to joules using \( E(J)=E(kWh)\times3.6\times 10^{6} \).

For part (iii), the monthly energy consumption for four bulbs is \( E_{monthly}=40P\times30 = 1200P \) kWh. The cost is then \( Cost = E_{monthly}\times0.15 \) dollars (since 15 cents = 0.15 dollars).

Answer:

To solve the problem, we need the power rating (in watts or kilowatts) of the LED light bulbs. Once we have that value (\( P \) in kW for part (i) and (iii), or \( P \) in watts which we can convert to kW), we can use the formula \( E = P\times t \) (and unit conversion for part (ii)) to find the energy consumption and cost.