Calculating the Length of a Heating Element Wire: A Practical Example

Introduction: Understanding the principles behind the resistance of a heating element is crucial for practical applications in electrical engineering, physics, and various industries. This article provides a detailed example of how to calculate the length of a heating element wire using the given parameters. By following the step-by-step guide, you can enhance your grasp of electrical resistivity and improve your problem-solving skills.

Understanding Resistance in a Heating Element

A heating element is a component that converts electrical energy into heat. The resistance of a heating element plays a significant role in determining the amount of heat produced. The resistance (R) of a wire is determined by several factors, including the resistivity (ρ), the length (L), and the cross-section area (A) of the wire. The relationship is defined by the formula:

Key Formulas:

Resistivity formula: [ R rho frac{L}{A} ]

Deriving the Length of a Heating Wire:

Given Parameters:

Resistance (R) 40 ohms Resistivity (ρ) 1.4×10-6 ohm·m Cross-section area (A) 0.0215 sq mm

Step-by-Step Solution:

The equation for resistance in a wire is: [ R rho frac{L}{A} ]

Rearranging this equation to solve for the length (L) gives us:

[ L frac{RA}{rho} ]

First, convert the cross-section area from sq mm to sq m:

[ A 0.0215 , text{sq mm} 0.0215 times 10^{-6} , text{sq m} 2.15 times 10^{-8} , text{sq m} ]

Substitute the given values into the equation:

[ L frac{40 times 2.15 times 10^{-8}}{1.4 times 10^{-6}} ]

Perform the multiplication in the numerator:

[ L frac{8.6 times 10^{-7}}{1.4 times 10^{-6}} ]

Finally, divide the result:

[ L frac{8.6}{1.4} times 10^{-1} , text{m} approx 6.14 times 10^{-1} , text{m} 0.614 , text{m} ]

Therefore, the length of the heating element wire is 0.614 meters.

Importance of Problem-Solving Skills

It's important to note that doing your own work is essential for learning and for future exercises. Writing simply is key: don't overcomplicate the problem. Let's break it down:

The equation we used for resistance is a fundamental property of materials and is crucial to understand. Converting units from millimeters squared to meters squared is a common practice that helps maintain consistency in calculations. By applying the resistivity formula, we can accurately determine the physical dimensions of a component, which is essential in real-world applications.

Conclusion

In conclusion, the length of the heating element wire is 0.614 meters. This example demonstrates the practical application of the resistance formula and the importance of converting units properly. Mastering these concepts will benefit your studies and future coursework in electrical engineering and related fields.