1. What is Electrical Resistance?

Electrical resistance is a measure of the opposition to current flow in an electrical circuit. It's measured in ohms (Ω) and depends on the material's properties and its physical dimensions.

2. Understanding the Resistance Formula

The resistance formula is:

Where:

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

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

3. Practical Applications

Details: This calculation is essential for designing electrical circuits, selecting appropriate wire gauges, creating resistors, and understanding material conductivity.

4. Using the Calculator

Tips: Enter resistivity in Ω·m (e.g., copper is 1.68×10⁻⁸ Ω·m), length in meters, and cross-sectional area in square meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between resistance and resistivity?
A: Resistivity (ρ) is an intrinsic property of the material, while resistance (R) depends on both the material and its dimensions.

Q2: Why does resistance increase with temperature?
A: For most conductors, increased temperature causes more atomic vibrations, which impede electron flow, increasing resistance.

Q3: What materials have the lowest resistivity?
A: Silver (1.59×10⁻⁸ Ω·m) and copper (1.68×10⁻⁸ Ω·m) have among the lowest resistivities at room temperature.

Q4: How does wire gauge affect resistance?
A: Thicker wires (larger gauge numbers) have greater cross-sectional area, resulting in lower resistance for a given length.

Q5: What is the resistance of a perfect conductor?
A: A perfect conductor would have zero resistance, though no real materials achieve this except superconductors at critical temperatures.