Question

Write the unit of specific resistance.

Hint:

Remember the distinction: Resistance (\(R\)) is a property of a specific object and depends on its shape and size, measured in ohms (\(\Omega\)). Resistivity (\(\rho\)) is a property of the material itself, measured in ohm-meters (\(\Omega \cdot m\)).

Answer 1

Step 1: Understanding the Concept:
Specific resistance, also known as resistivity, is an intrinsic property of a material that quantifies how strongly it resists the flow of electric current. It is denoted by the Greek letter \(\rho\) (rho).

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

Step 3: Detailed Explanation:
To find the unit of resistivity, we can substitute the SI units for the quantities on the right side of the rearranged formula: \begin{itemize} \item The unit of resistance (\(R\)) is the ohm (\(\Omega\)).
\item The unit of area (\(A\)) is the square meter (\(m^2\)).
\item The unit of length (\(L\)) is the meter (\(m\)).
\end{itemize} Substituting these units into the equation for \(\rho\): \[ \text{Unit of } \rho = \frac{\text{Unit of } R \times \text{Unit of } A}{\text{Unit of } L} = \frac{\Omega \cdot m^2}{m} \] Simplifying the expression, we get: \[ \text{Unit of } \rho = \Omega \cdot m \]

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