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: Formula for resistance and resistivity
The resistivity (\( \rho \)) of a material is related to its resistance (\( R \)), length (\( l \)), and cross-sectional area (\( A \)) by the formula:
\[ R = \rho \frac{l}{A} \]

Step 2: Rearranging the formula to find resistivity
To find the resistivity, we can rearrange the formula as follows:
\[ \rho = R \frac{A}{l} \]

Step 3: SI units of each quantity
- The SI unit of resistance (\( R \)) is the ohm (\( \Omega \)).
- The SI unit of area (\( A \)) is the square meter (\( \text{m}^2 \)).
- The SI unit of length (\( l \)) is the meter (\( \text{m} \)).

Step 4: Calculating the SI unit of resistivity
Now, we substitute the SI units of \( R \), \( A \), and \( l \) into the formula for resistivity:
\[ \rho = \Omega \times \frac{\text{m}^2}{\text{m}} \] This simplifies to:
\[ \rho = \Omega \, \text{m} \]

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