Understanding the Energy Consumption of an Electric Kettle with 25 Ohms Resistance

Electric kettles are a common household appliance used for boiling water efficiently. When it comes to understanding their energy consumption, particularly in scenarios where specific parameters such as resistance and current are known, the calculations can be straightforward but informative. This article will delve into how to calculate the energy consumed by an electric kettle with a resistance of 25 ohms over a period of 12 hours, using basic principles of electrical engineering.

Key Concepts: Ohms Law and Power Formula

To effectively calculate the energy consumption of an electric kettle, it is essential to have a basic understanding of a few key concepts. These include Ohms law and the power formula.

Ohms Law

Ohms law states that the voltage (V) across a resistor is equal to the current (I) through the resistor multiplied by the resistance (R). Mathematically, it can be expressed as:

V I x R

Given that our electric kettle has a resistance of 25 ohms (Ω) and a current of 2 amperes (A), we can calculate the voltage as follows:

V 2 A x 25 Ω 50 V

Power Formula

Power is the rate at which energy is consumed or dissipated. In the context of an electric kettle, the power (P) can be calculated using several formulas. One of the most useful formulas is:

P V x I I^2 x R

Using the values provided:

Voltage (V) 50 V Current (I) 2 A Resistance (R) 25 Ω

Calculating Power Using Ohms Law

The power consumed by the kettle can be calculated as:

P V x I 50 V x 2 A 100 W

Directly using Resistance

Alternatively, we can use the second formula:

P I^2 x R (2 A)^2 x 25 Ω 4 A^2 x 25 Ω 100 W

Calculating Energy Consumption Over 12 Hours

Once we have determined the power consumed by the kettle, we can calculate the energy consumed over a specific period. The energy (E) consumed is given by the formula:

E P x Time

In this case, the time is 12 hours (or 12 x 3600 seconds).

Converting Power to Energy

To find the total energy consumed, we multiply the power by the time:

E 100 W x 12 hours 1200 Wh

Converting to Kilowatt Hours

To convert the energy from watt-hours (Wh) to kilowatt-hours (kWh), we divide by 1000:

E 1200 Wh / 1000 1.2 kWh

Thus, the energy consumed by the kettle in 12 hours is 1.2 kWh.

Practical Consideration: Cost of Electricity Usage

Understanding the energy consumption is not just theoretical. It also has practical implications, particularly in terms of the cost of electricity. To determine the cost, you need to know the rate at which your electricity supplier charges you for each kilowatt hour (kWh). The formula to calculate the cost is:

Cost Energy used (kWh) x Rate per kWh

For example, if your electricity rate is 0.15 dollars per kWh, the cost of using the kettle for 12 hours would be:

Cost 1.2 kWh x 0.15 dollars/kWh 0.18 dollars

Conservation of Energy in Electric Kettles

From the law of conservation of energy, we know that the energy dissipated by the kettle is equal to the energy it consumes over a given period. The power dissipated by a purely resistive load can be calculated using the formula:

Power I^2 x R 2^2 A^2 x 25 Ω 100 W

The energy dissipated can be calculated as:

Energy Power x Time 100 W x 43200 s 4320000 J 4.32 x 10^6 J 1.2 kWh

This confirms that the energy calculated using the formula for power is the same as the energy consumed over 12 hours.

Conclusion

By understanding the principles of Ohms law and the power formula, you can easily calculate the energy consumption of an electric kettle. Whether for theoretical understanding or practical purposes such as calculating electricity costs, knowing these calculations can be invaluable. Remember, the key is in the application of the right formulas and a clear understanding of the relationships between voltage, current, and resistance.

References

[1] Ohm’s Law and Electrical Power: A Comprehensive Guide.

[2] Basic Electrical Calculations: Energy and Power.