1. What is the Resistance Formula?

The resistance formula \( R = \rho \frac{L}{A} \) calculates the electrical resistance of a conductor based on its material properties and physical dimensions. It shows how resistance depends on resistivity, length, and cross-sectional area.

2. How Does the Calculator Work?

The calculator uses the resistance formula:

Where:

• \( R \) — Electrical resistance (ohms, Ω)
• \( \rho \) — Resistivity of the material (Ω·m)
• \( L \) — Length of the conductor (m)
• \( A \) — Cross-sectional area of the conductor (m²)

Explanation: The formula demonstrates that resistance is directly proportional to both resistivity and length, but inversely proportional to cross-sectional area.

3. Importance of Resistance Calculation

Details: Accurate resistance calculation is crucial for designing electrical circuits, selecting appropriate wire sizes, calculating power losses, and ensuring proper functioning of electrical systems.

4. Using the Calculator

Tips: Enter resistivity in Ω·m, length in meters, and cross-sectional area in square meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is resistivity?
A: Resistivity is an intrinsic property of materials that quantifies how strongly they oppose electric current. Different materials have different resistivity values.

Q2: Why does resistance increase with length?
A: Longer conductors provide more opposition to electron flow because electrons must travel through more material, encountering more collisions.

Q3: Why does resistance decrease with larger cross-sectional area?
A: Larger cross-sectional areas provide more pathways for electrons to flow, reducing the overall opposition to current.

Q4: What are typical resistivity values?
A: Copper: ~1.68×10⁻⁸ Ω·m, Aluminum: ~2.82×10⁻⁸ Ω·m, Silver: ~1.59×10⁻⁸ Ω·m, Iron: ~1.0×10⁻⁷ Ω·m.

Q5: How does temperature affect resistance?
A: For most conductors, resistance increases with temperature due to increased atomic vibrations that impede electron flow.