Understanding the Resistance of a Wire Divided into Four Equal Parts

When a copper wire with resistance R is cut into four equal parts, how does the resistance change? This is a fundamental question in electrical engineering and physics, often seen in textbooks and practical applications. We will explore the underlying principles, formulas, and practical implications of this scenario.

Factors Affecting Wire Resistance

Wire resistance is primarily determined by its gauge (size) and the material it is made of. For copper wire, the gauge is expressed using the American Wire Gauge (AWG) system. Smaller AWG numbers correspond to larger wire diameters. For example, a #10 AWG wire can handle 30 amps, while a #18 AWG wire can support only 6 amps. These differences are crucial to understand when designing electrical systems, as they directly impact the current-carrying capacity and voltage requirements.

The Fundamental Formula

The resistance R of a wire can be calculated using the formula:

R ρL/A

Where:

R is the resistance of the wire (Ohms, Ω) ρ (rho) is the resistivity of the material (Ohm-meters, Ω·m) L is the length of the wire (meters, m) A is the cross-sectional area of the wire (square meters, m2)

When a wire is cut into four equal parts, the length L of each part becomes 1/4 of the original length. The cross-sectional area A remains the same if the diameter is unchanged. Therefore, the resistance of each part will be R/4.

Theoretical Explanation

If the original wire has a total resistance of R, and it is cut into four equal parts, each segment will have a resistance of R/4. This is because the resistance is directly proportional to the length of the wire. If the wire is equally divided, each segment will have a quarter of the original length, leading to a quarter of the original resistance. Mathematically, this can be represented as:

R/4 R/4×1/4 R/16

This means that the total resistance of the four segments connected in series would be:

R R/4 R/4 R/4 R/4 4 × (R/4) R

Each segment's resistance is R/4, and when connected in series, the total resistance remains R.

Practical Applications and Resources

Wire resistance is crucial in various applications, such as audio wiring, power distribution, and telecommunications. For professionals in these fields, a reliable resource is essential. Websites like Belden, Canare, and Mogami offer extensive information on wire specifications and resistances. Belden, in particular, is highly regarded due to its consistent performance and reliability.

Conclusion

The resistance of a wire divided into four equal parts is known to be reduced to one-fourth of the original resistance. This is based on the fundamental principles of electrical resistance, the resistivity of the material, and the length-to-area ratio of the wire. Understanding these concepts is essential for any engineer or technician working with electrical systems.

Further Reading

For more in-depth information on wire resistance and related topics, explore the following resources:

Belden Learning Center: Basics of Electrical Wiring Canare: Technical Brochure on Electrical Performance Mogami: Resources and Articles on Wire and Cable Technology