An electric lamp of 100 W is used for 5 hours per day. How much energy will be consumed by the lamp for 3 days?
1.5 units
Calculating Electric Energy Consumption
Understanding how to calculate energy consumption for electrical appliances is an important concept. Energy is consumed when power is used over a period of time. The standard unit for electrical energy consumption is the kilowatt-hour (kWh), often referred to simply as a 'unit'.
Problem Analysis: Electric Lamp Energy Use
The problem asks us to find the total energy consumed by an electric lamp with a given power rating over a specific duration. Here's what we know:
- Power of the electric lamp = 100 W
- Daily usage time = 5 hours
- Number of days the lamp is used = 3 days
We need to calculate the total energy consumed by this lamp over the 3-day period and express it in 'units' (kWh).
Steps to Calculate Energy Consumption
To find the total energy consumed, we follow these steps:
- Calculate the total time the lamp is used over the entire period.
- Convert the power of the lamp from Watts (W) to Kilowatts (kW).
- Calculate the energy consumed using the formula: Energy = Power × Time.
Step 1: Calculate Total Usage Time
The lamp is used for 5 hours each day for 3 days. The total time it is switched on is:
Total time = Daily usage time × Number of days
Total time = \(5 \text{ hours/day} \times 3 \text{ days}\)
Total time = \(15 \text{ hours}\)
Step 2: Convert Power from Watts to Kilowatts
Energy consumption in 'units' (kWh) requires power to be in kilowatts (kW) and time in hours. The power of the lamp is given in Watts (W). We need to convert 100 W to kW.
There are 1000 Watts in 1 Kilowatt.
Power in kW = Power in W / 1000
Power in kW = \(100 \text{ W} / 1000\)
Power in kW = \(0.1 \text{ kW}\)
Step 3: Calculate Total Energy Consumed
Now we can use the formula for energy consumption:
Energy = Power (kW) × Total time (hours)
Energy = \(0.1 \text{ kW} \times 15 \text{ hours}\)
Energy = \(1.5 \text{ kWh}\)
Since 1 kWh is equal to 1 unit, the total energy consumed is 1.5 units.
Let's summarize the calculation:
| Parameter | Value |
|---|---|
| Lamp Power | 100 W = 0.1 kW |
| Daily Usage | 5 hours/day |
| Number of Days | 3 days |
| Total Usage Time | \(5 \times 3 = 15\) hours |
| Energy Consumed | \(0.1 \text{ kW} \times 15 \text{ hours} = 1.5 \text{ kWh}\) |
| Energy Consumed (Units) | 1.5 units |
Comparing with Options
The calculated energy consumption is 1.5 units. Let's look at the provided options:
- 1.5 units
- 5.0 units
- 0.5 units
- 1.0 units
Our calculated value matches the first option.
Conclusion on Electric Energy Consumption
By converting the power to kilowatts and multiplying by the total time in hours, we found that the electric lamp consumes 1.5 kilowatt-hours, or 1.5 units of energy, over the 3-day period.
Revision Table: Energy Consumption Calculation
| Concept | Formula/Relation | Units |
|---|---|---|
| Energy (E) | \(E = P \times t\) | Joules (J) or kilowatt-hours (kWh) |
| Power (P) | Rate of energy transfer | Watts (W) or Kilowatts (kW) |
| Time (t) | Duration of energy transfer | Seconds (s) or Hours (h) |
| Conversion: W to kW | \(1 \text{ kW} = 1000 \text{ W}\) | - |
| Conversion: kWh to Units | \(1 \text{ kWh} = 1 \text{ unit}\) | - |
Additional Information: Understanding Kilowatt-Hours (kWh)
The kilowatt-hour (kWh) is a commonly used unit of electrical energy. It represents the energy consumed by a device with a power of 1 kilowatt operating for 1 hour. Electricity bills are typically based on the number of kWh consumed.
- Why kWh? Using kWh is convenient for billing purposes because common household appliances have power ratings in watts or kilowatts and are used for durations measured in hours. Calculating energy in Joules (the SI unit of energy) would involve very large numbers since 1 kWh = \(3.6 \times 10^6\) Joules.
- Appliance Rating: Appliance power ratings (like 100 W for the lamp in the question) indicate how much power they consume when in use. Higher wattage means higher power consumption.
- Calculating Cost: If the cost of electricity per unit (kWh) is known, the total electricity bill for an appliance can be calculated by multiplying the total kWh consumed by the cost per unit.
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