Question

Write the relation between resistivity (\(\rho\)) and resistance (\(R\)) for a uniform metallic conductor of length (\(l\)) and area of cross-section (\(A\)). Use this relation to obtain the SI unit of resistivity.

Answer 1

Step 1: Resistance and Resistivity Formula
Resistivity (\( \rho \)) is linked to resistance (\( R \)), length (\( l \)), and cross-sectional area (\( A \)) by:
\[R = \rho \frac{l}{A}\]

Step 2: Rearranging for Resistivity
To solve for resistivity, the formula becomes:
\[\rho = R \frac{A}{l}\]

Step 3: SI Units of Components
- Resistance (\( R \)): Ohm (\( \Omega \))
- Area (\( A \)): Square meter (\( \text{m}^2 \))
- Length (\( l \)): Meter (\( \text{m} \))

Step 4: Calculating Resistivity's SI Unit
Substituting the SI units into the resistivity formula:
\[\rho = \Omega \times \frac{\text{m}^2}{\text{m}}\] This simplifies to:
\[\rho = \Omega \, \text{m}\]

Final Answer:
The SI unit of resistivity is \( \Omega \, \text{m} \) (ohm-meter).