1. What is Resistance and Resistivity?

Resistivity (ρ) is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. Resistance (R) is the actual opposition to current flow in a specific conductor, which depends on both the material's resistivity and its geometry.

2. How Does the Formula Work?

The resistance formula is:

Where:

• \( R \) — Resistance in ohms (Ω)
• \( \rho \) — Resistivity in ohm-meters (Ω·m)
• \( L \) — Length of conductor in meters (m)
• \( A \) — Cross-sectional area in square meters (m²)

Explanation: Resistance increases with length (more material for electrons to travel through) and decreases with cross-sectional area (more paths for electrons to flow).

3. Importance of Resistance Calculation

Details: Calculating resistance is fundamental in designing electrical circuits, selecting appropriate wire gauges, and understanding power dissipation in components.

4. Using the Calculator

Tips: Enter resistivity in Ω·m, length in meters, and cross-sectional area in m². All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between resistance and resistivity?
A: Resistivity is a material property, while resistance depends on both the material and its dimensions.

Q2: What are typical resistivity values?
A: Copper: ~1.68×10⁻⁸ Ω·m; Silicon: ~2.3×10³ Ω·m; Glass: ~10¹⁰ to 10¹⁴ Ω·m.

Q3: How does temperature affect resistivity?
A: For metals, resistivity increases with temperature. For semiconductors, it generally decreases.

Q4: Can this formula be used for any shape?
A: It works for uniform cross-sections. For complex shapes, integration may be needed.

Q5: What about AC resistance?
A: At high frequencies, skin effect increases effective resistance, requiring modified calculations.