A 100 W electric bulb is used for 10 hours a day. How many units of electrical energy are consumed by the bulb in 3 days? (1 unit = 1 kWh)
3.00
Calculating Electrical Energy Consumption
This question asks us to calculate the total electrical energy consumed by an electric bulb over a specific period and express it in 'units', where 1 unit is equal to 1 kilowatt-hour (kWh).
Electrical energy consumption depends on two main factors: the power of the appliance and the duration for which it is used.
The formula to calculate electrical energy is:
Energy = Power × Time
Let's break down the given information and perform the calculation step-by-step.
- Power of the bulb: The electric bulb has a power rating of 100 W.
- Daily usage time: The bulb is used for 10 hours each day.
- Total number of days: The calculation needs to be done for 3 days.
- Unit of energy: 1 unit = 1 kWh.
Step-by-Step Energy Calculation
Step 1: Convert Power to Kilowatts (kW)
The power is given in Watts (W), but the energy unit (kWh) requires power in Kilowatts (kW). We know that 1 kW = 1000 W.
Power in kW = Power in W / 1000
Power of the bulb = 100 W / 1000 W/kW = 0.1 kW
Step 2: Calculate Total Usage Time
The bulb is used for 10 hours per day for 3 days. We need the total hours of usage over this period.
Total Time = Daily usage time × Number of days
Total Time = 10 hours/day × 3 days = 30 hours
Step 3: Calculate Total Electrical Energy Consumed
Now we can use the formula Energy = Power × Time, using the values in kW and hours.
Total Energy Consumed (in kWh) = Power (in kW) × Total Time (in hours)
Total Energy Consumed = 0.1 kW × 30 hours = 3 kWh
Step 4: Convert Energy from kWh to Units
The question specifies that 1 unit = 1 kWh. Therefore, the energy consumed in units is the same as the energy consumed in kWh.
Energy in Units = Energy in kWh / (1 kWh/unit)
Energy in Units = 3 kWh / 1 kWh/unit = 3 units
So, the electric bulb consumes 3 units of electrical energy in 3 days.
Summary of Calculations
| Parameter | Value | Unit |
|---|---|---|
| Power of bulb | 100 | W |
| Power of bulb (converted) | 0.1 | kW |
| Daily usage | 10 | hours/day |
| Number of days | 3 | days |
| Total usage time | 30 | hours |
| Total energy consumed | 3 | kWh |
| Energy consumed in units (1 unit = 1 kWh) | 3 | units |
Comparing our calculated value with the given options, we find that 3.00 units matches one of the options.
Revision Table: Electrical Energy Basics
| Concept | Definition/Formula | Unit(s) |
|---|---|---|
| Electric Power (P) | Rate at which electrical energy is transferred or used. | Watt (W), Kilowatt (kW) |
| Electric Energy (E) | Power used over a period of time. \(E = P \times T\) | Joule (J), Watt-hour (Wh), Kilowatt-hour (kWh) |
| Kilowatt-hour (kWh) | Energy consumed by a device of 1 kW power operating for 1 hour. | kWh |
| 'Unit' of Energy | Commonly used term for 1 kWh in electricity billing. | Unit |
Additional Information: Understanding Electrical Units
The kilowatt-hour (kWh) is the standard unit used by electricity providers to bill consumers. This is why calculating energy consumption in kWh is important for understanding electricity costs. The term 'unit' is simply a common name for 1 kWh on your electricity meter and bill.
The power rating of an appliance, usually given in Watts (W), indicates how much energy it consumes per unit of time when in operation. Higher wattage appliances consume energy at a faster rate.
Calculating energy consumption helps in understanding which appliances use the most energy and can guide efforts to save electricity and reduce bills.
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