Understanding Specific Resistance (Resistivity)

Specific resistance, also known as resistivity, is a fundamental property of a material that measures how strongly it resists electric current. Unlike resistance, which depends on the dimensions (length and cross-sectional area) of a conductor, specific resistance is an intrinsic property of the material itself at a given temperature.

Formula for Specific Resistance

The relationship between resistance ($R$), specific resistance ($\rho$), length ($L$), and cross-sectional area ($A$) of a conductor is given by the formula:

\begin{equation*}\rho = \frac{RA}{L}\end{equation*}

Where:

• $R$ is the resistance of the conductor
• $\rho$ (rho) is the specific resistance (resistivity)
• $A$ is the cross-sectional area of the conductor
• $L$ is the length of the conductor

Deriving the Unit of Specific Resistance

To find the unit of specific resistance, we can substitute the standard units of the other quantities into the formula:

• The unit of resistance ($R$) is Ohm ($\Omega$).
• The unit of cross-sectional area ($A$) is square meter ($m^2$).
• The unit of length ($L$) is meter ($m$).

Substituting these units into the formula $\rho = \frac{RA}{L}$, we get:

Unit of $\rho$ = $\frac{\text{Unit of } R \times \text{Unit of } A}{\text{Unit of } L}$

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

When we simplify the units, $m^2/m$ becomes $m$.

So, the unit of specific resistance is $\Omega \cdot m$, which is read as Ohm-meter.

Conclusion on the Unit of Specific Resistance

Based on the derivation from the formula, the unit of specific resistance (resistivity) is Ohm-meter ($\Omega \cdot m$). This unit represents the resistance of a material with a standard length (1 meter) and a standard cross-sectional area (1 square meter).

Looking at the options provided:

• Option 1: Ohm ($\Omega$) is the unit of resistance, not specific resistance.
• Option 2: Ohm-meter ($\Omega \cdot m$) is the derived unit of specific resistance.
• Option 3: Ohm/meter ($\Omega/m$) is not the correct unit for specific resistance.
• Option 4: Ohm/meter² ($\Omega/m^2$) is also not the correct unit for specific resistance.

Therefore, the correct unit of specific resistance is Ohm-meter.