Home
Back
Resistance Formula:
| From: | To: |
The resistance formula \( R = \frac{L}{\sigma A} \) calculates the electrical resistance of a material based on its physical dimensions and conductivity properties. This fundamental equation relates resistance to length, conductivity, and cross-sectional area.
The calculator uses the resistance formula:
Where:
Explanation: The formula shows that resistance is directly proportional to length and inversely proportional to both conductivity and cross-sectional area.
Details: Accurate resistance calculation is crucial for electrical circuit design, material selection, power transmission systems, and electronic device manufacturing. It helps engineers optimize performance and efficiency.
Tips: Enter length in meters, conductivity in siemens per meter (S/m), and cross-sectional area in square meters (m²). All values must be positive numbers greater than zero.
Q1: What Is The Difference Between Conductivity And Resistivity?
A: Conductivity (σ) is the reciprocal of resistivity (ρ). The relationship is \( \sigma = \frac{1}{\rho} \), and the resistance formula can also be written as \( R = \rho \frac{L}{A} \).
Q2: How Does Temperature Affect Resistance?
A: For most conductors, resistance increases with temperature due to decreased conductivity. The temperature coefficient of resistance quantifies this relationship.
Q3: What Are Typical Conductivity Values For Common Materials?
A: Silver (~6.3×10⁷ S/m), Copper (~5.96×10⁷ S/m), Gold (~4.5×10⁷ S/m), Aluminum (~3.5×10⁷ S/m). Insulators have much lower conductivity values.
Q4: When Is This Formula Most Accurate?
A: This formula is most accurate for uniform materials with constant cross-section at constant temperature. It assumes homogeneous material properties.
Q5: How Does Cross-sectional Area Affect Resistance?
A: Resistance decreases as cross-sectional area increases. Doubling the area halves the resistance, making thicker wires better conductors.