A 100 W electric bulb is used for 10 hours a day. How many units of energy are consumed in 30 days?
30
Understanding Electric Energy Consumption
The question asks us to calculate the total energy consumed by an electric bulb over a specific period and express it in 'units'. In the context of electricity billing, a 'unit' of energy refers to one kilowatt-hour (kWh).
Given Information
- Power of the electric bulb = 100 Watts (W)
- Daily usage time = 10 hours per day
- Total number of days = 30 days
Calculating Energy Consumption
Energy consumed is calculated by multiplying the power of the appliance by the time it is used. The formula is:
Energy = Power × Time
To get the energy in kilowatt-hours (kWh), the power must be in kilowatts (kW) and the time in hours (h).
Step 1: Convert Power to Kilowatts
The power is given in Watts. We need to convert it to Kilowatts. There are 1000 Watts in 1 Kilowatt.
\[ \text{Power in kW} = \frac{\text{Power in W}}{1000} \]
\[ \text{Power in kW} = \frac{100 \text{ W}}{1000} = 0.1 \text{ kW} \]
So, the power of the bulb is 0.1 kW.
Step 2: Calculate Daily Energy Consumption
Now we calculate the energy consumed by the bulb in one day. The bulb is used for 10 hours a day at a power of 0.1 kW.
\[ \text{Daily Energy Consumption} = \text{Power in kW} \times \text{Time in hours per day} \]
\[ \text{Daily Energy Consumption} = 0.1 \text{ kW} \times 10 \text{ hours/day} = 1 \text{ kWh/day} \]
Since 1 kWh is equal to 1 unit of energy, the bulb consumes 1 unit of energy per day.
Step 3: Calculate Total Energy Consumption over 30 Days
To find the total energy consumed over 30 days, we multiply the daily energy consumption by the number of days.
\[ \text{Total Energy Consumption} = \text{Daily Energy Consumption} \times \text{Number of Days} \]
\[ \text{Total Energy Consumption} = 1 \text{ kWh/day} \times 30 \text{ days} = 30 \text{ kWh} \]
Therefore, the total energy consumed in 30 days is 30 kWh.
Converting Total Energy to Units
As established, 1 unit of energy is equal to 1 kWh.
Total energy consumed = 30 kWh = 30 units.
The total number of units of energy consumed in 30 days is 30.
Summary of Calculation
| Parameter | Value | Unit |
|---|---|---|
| Power of bulb | 100 | W |
| Power of bulb (converted) | 0.1 | kW |
| Daily usage time | 10 | hours |
| Number of days | 30 | days |
| Daily Energy Consumption | \(0.1 \text{ kW} \times 10 \text{ h} = 1\) | kWh (unit) |
| Total Energy Consumption (30 days) | \(1 \text{ kWh/day} \times 30 \text{ days} = 30\) | kWh (units) |
Conclusion on Energy Consumption
Based on the calculations, the electric bulb consumes 30 units of energy over a period of 30 days when used for 10 hours daily.
Revision Table: Energy and Power Concepts
| Concept | Definition | Formula | Standard Units |
|---|---|---|---|
| Power (P) | The rate at which energy is transferred or used. | \(P = \frac{E}{t}\) | Watt (W), Kilowatt (kW) |
| Energy (E) | The capacity to do work. | \(E = P \times t\) | Joule (J), Watt-hour (Wh), Kilowatt-hour (kWh) |
| Time (t) | Duration over which power is used. | - | Seconds (s), Hours (h) |
| 1 Kilowatt-hour (kWh) | The energy consumed by a 1 kW device operating for 1 hour. Also known as 1 'unit' of electricity. | \(1 \text{ kWh} = 1000 \text{ Wh}\) \(1 \text{ kWh} = 3.6 \times 10^6 \text{ J}\) |
kWh (unit) |
Additional Information on Electricity Units
Understanding how electricity consumption is measured is important for managing electricity bills. The term 'unit' is commonly used by electricity providers to measure the energy consumed by households and businesses. This 'unit' is equivalent to one kilowatt-hour (kWh).
For example, if you use a 1000 Watt (1 kW) appliance for 1 hour, you consume 1 kWh or 1 unit of electricity. If you use a 2000 Watt (2 kW) appliance for 30 minutes (0.5 hours), you consume \(2 \text{ kW} \times 0.5 \text{ h} = 1 \text{ kWh}\) or 1 unit.
Knowing the power rating of your appliances and how long you use them helps you estimate your monthly electricity consumption in units, which directly relates to the cost on your electricity bill.
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