Question

The unit of resistivity in a conductor is

• A. \(\Omega\) m
• B. \(\Omega\)/m
• C. \(\Omega^{-1}\)
• D. None of these

Hint:

Don't confuse resistance and resistivity. Resistance is a property of an object (e.g., a wire), while resistivity is a property of the material the object is made of (e.g., copper).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Resistivity (symbol \(\rho\)) is a fundamental property of a material that quantifies how strongly it resists the flow of electric current. It is different from resistance (R), which depends on the material's shape and size.

Step 2: Key Formula or Approach:
The resistance (R) of a conductor is related to its resistivity (\(\rho\)), length (L), and cross-sectional area (A) by the formula:
\[ R = \rho \frac{L}{A} \]

Step 3: Detailed Explanation:
To find the unit of resistivity (\(\rho\)), we can rearrange the formula:
\[ \rho = R \frac{A}{L} \] Now, let's substitute the SI units for each quantity:
\[\begin{array}{rl} \bullet & \text{Unit of Resistance (R) is Ohm (\(\Omega\)). } \\ \bullet & \text{Unit of Area (A) is square meter (\(m^2\)). } \\ \bullet & \text{Unit of Length (L) is meter (m). } \\ \end{array}\] Substituting these into the rearranged formula:
\[ \text{Unit of } \rho = \Omega \frac{m^2}{m} = \Omega \cdot m \] The unit \(\Omega^{-1}\) is the unit of conductance, Siemens (S).

Step 4: Final Answer:
The SI unit of resistivity is the Ohm-meter (\(\Omega\) m).