Understanding Specific Resistance and its SI Unit

The question asks us to determine the standard International System of Units (SI) unit for specific resistance, often denoted by the Greek letter rho ($\rho$). We are given the relationship between electrical resistance ($R$), the material's length ($L$), its uniform cross-sectional area ($A$), and its specific resistance ($\rho$):

$R = \rho \frac{L}{A}$

We are also provided with the standard SI units for the other quantities involved:

• Electrical Resistance ($R$): Ohms ($\Omega$)
• Length ($L$): meters ($m$)
• Cross-sectional Area ($A$): square meters ($m^2$)

Deriving the Formula for Specific Resistance

To find the unit of specific resistance ($\rho$), we need to rearrange the given formula to isolate $\rho$. Multiplying both sides by $A$ and dividing by $L$, we get:

$\rho = R \frac{A}{L}$

Calculating the SI Unit of Specific Resistance

Now, we can substitute the SI units of $R$, $A$, and $L$ into the rearranged formula to find the unit of $\rho$.

Unit of $\rho$ = (Unit of $R$) $\times$ (Unit of $A$) / (Unit of $L$)

Substituting the given units:

Unit of $\rho$ = $\Omega \times \frac{m^2}{m}$

Simplifying the expression:

Unit of $\rho$ = $\Omega \times m$

Conclusion on Specific Resistance Unit

Therefore, the standard SI unit for specific resistance ($\rho$) is Ohm-meter, which is written as $\Omega \cdot m$. This unit correctly reflects the relationship between resistance, length, and area for a given material.

Comparing this result with the given options, the correct unit for specific resistance is Ohm-meter ($\Omega \cdot m$).