A 60 watt incandescent light bulb is left on for 5 hours. How many hours will it take for a 15 watt compact fluorescent bulb to consume the same amount of energy?
a. 4
b. 12
c. 20
d. 75
The correct answer and explanation is:
To find how long it would take for the 15-watt compact fluorescent bulb to consume the same amount of energy as a 60-watt incandescent light bulb, we first need to calculate the energy consumed by the incandescent bulb.
The energy consumed by a light bulb can be calculated using the formula: E=P×tE = P \times t
where:
- EE is the energy in watt-hours (Wh),
- PP is the power in watts (W),
- tt is the time in hours (h).
Step 1: Calculate energy used by the incandescent bulb.
The incandescent bulb is 60 watts, and it is left on for 5 hours. So, E=60 W×5 h=300 Wh.E = 60 \, \text{W} \times 5 \, \text{h} = 300 \, \text{Wh}.
This means the incandescent bulb uses 300 watt-hours of energy in 5 hours.
Step 2: Calculate how long it will take for the 15-watt compact fluorescent bulb to use 300 watt-hours.
Now, we need to calculate the time tt it would take for the 15-watt compact fluorescent bulb to consume 300 watt-hours of energy. Rearranging the energy formula: t=EPt = \frac{E}{P}
Substitute E=300 WhE = 300 \, \text{Wh} and P=15 WP = 15 \, \text{W}: t=300 Wh15 W=20 hours.t = \frac{300 \, \text{Wh}}{15 \, \text{W}} = 20 \, \text{hours}.
Conclusion:
It will take 20 hours for the 15-watt compact fluorescent bulb to consume the same amount of energy as the 60-watt incandescent bulb.
So, the correct answer is c. 20 hours.