Understanding the Electric Kettle Problem

The question asks us to find the cost of operating an electric kettle. We are given the following information:

• Power rating of the kettle: 2.2 kW
• Voltage rating: 220V (This information is not needed for the cost calculation itself but is part of the kettle's specifications)
• Time duration of operation: 30 minutes
• Cost of electricity: ₹4 per unit (kWh)

Our goal is to calculate the total cost based on the energy consumed during the 30 minutes of operation.

Calculating Energy Consumption

First, we need to calculate the amount of electrical energy the kettle consumes. The formula relating energy, power, and time is:

\(E = P \times t\)

Where:

• $E$ is the energy consumed (in kilowatt-hours, kWh)
• $P$ is the power rating (in kilowatts, kW)
• $t$ is the time duration (in hours, h)

We are given the power $P$ as 2.2 kW. The time is given as 30 minutes. We need to convert this time into hours:

\(t = \frac{30 \text{ minutes}}{60 \text{ minutes/hour}} = 0.5 \text{ hours}\)

Now, we can calculate the energy consumed:

\(E = 2.2 \text{ kW} \times 0.5 \text{ h}\)

\(E = 1.1 \text{ kWh}\)

So, the electric kettle consumes 1.1 kWh of energy when used for 30 minutes.

Determining the Total Cost

The cost of electricity is given as ₹4 per unit, where one unit is equal to 1 kWh. To find the total cost, we multiply the energy consumed (in kWh) by the cost per unit.

The formula for the total cost is:

\(Total Cost = Energy Consumed (in kWh) \times Cost per Unit (in ₹/kWh)\)

Using the values we have:

\(Total Cost = 1.1 \text{ kWh} \times ₹4/\text{kWh}\)

$Total Cost = ₹4.4$

Summary of Calculation

• Power (P): 2.2 kW
• Time (t): 30 minutes = 0.5 hours
• Energy Consumed (E = P × t): 2.2 kW × 0.5 h = 1.1 kWh
• Cost per Unit: ₹4/kWh
• Total Cost (E × Cost Rate): 1.1 kWh × ₹4/kWh = ₹4.4

Therefore, the cost of boiling water for 30 minutes using the electric kettle is ₹4.4.