Question

SI unit of electrical resistivity is

• A. \( \Omega \, m \)
• B. \( \Omega / m \)
• C. \( m / \Omega \)
• D. \( \Omega \, m^2 \)

Hint:

Remember the formula \( R = \rho \frac{l}{A} \) and the SI units of resistance, length, and area to derive the SI unit of resistivity.

Answer 1

The Correct Option is A

Step 1: Recall the relationship between resistance, resistivity, length, and cross-sectional area of a conductor.
The resistance \( R \) of a conductor is given by the formula: \[ R = \rho \frac{l}{A} \] where \( \rho \) is the electrical resistivity of the material, \( l \) is the length of the conductor, and \( A \) is the cross-sectional area of the conductor. 

Step 2: Rearrange the formula to solve for resistivity \( \rho \). \[ \rho = \frac{RA}{l} \] 

Step 3: Identify the SI units of resistance, area, and length.
Resistance \( R \) is measured in Ohms (\( \Omega \)).
Cross-sectional area \( A \) is measured in square meters (\( m^2 \)).
Length \( l \) is measured in meters (\( m \)).

Step 4: Substitute the SI units into the formula for resistivity. \[ [\rho] = \frac{[\Omega] [m^2]}{[m]} \] \[ [\rho] = \Omega \cdot m \] The SI unit of electrical resistivity is Ohm-meter (\( \Omega \, m \)).