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Dimensional Formula:
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Electrical resistivity (ρ) is a fundamental property of materials that quantifies how strongly they oppose the flow of electric current. It is defined as the resistance between opposite faces of a unit cube of the material.
The dimensional formula for electrical resistivity is:
Where:
Explanation: This dimensional formula represents how resistivity depends on fundamental physical quantities. The positive exponents indicate direct proportionality, while negative exponents indicate inverse relationships.
Details: Dimensional analysis helps verify equations, derive relationships between physical quantities, and understand the fundamental nature of physical laws. It ensures consistency in physical equations and helps in unit conversions.
Tips: Enter values for mass (kg), length (m), time (s), and current (A). The calculator will compute the dimensional value of electrical resistivity in ohm-meters (Ω·m).
Q1: What is the SI unit of electrical resistivity?
A: The SI unit of electrical resistivity is ohm-meter (Ω·m).
Q2: How is resistivity different from resistance?
A: Resistivity is an intrinsic property of the material, while resistance depends on both the material and its dimensions (length and cross-sectional area).
Q3: What are typical resistivity values for common materials?
A: Conductors (copper): ~1.68×10⁻⁸ Ω·m, Semiconductors (silicon): ~2.3×10³ Ω·m, Insulators (glass): ~10¹⁰-10¹⁴ Ω·m.
Q4: Why does resistivity have negative time and current exponents?
A: The negative exponents indicate inverse relationships - resistivity decreases with increasing time and current in the dimensional analysis context.
Q5: How is dimensional formula derived for resistivity?
A: Starting from R = ρL/A and using Ohm's law V=IR, then substituting dimensions for voltage [ML²T⁻³I⁻¹] and solving for ρ gives the dimensional formula.