Unit of Resistivity Explained
Resistivity, often represented by the Greek letter rho ($\rho$), is a fundamental property of a material that quantifies how strongly it resists the flow of electric current. It's an intrinsic characteristic, meaning it depends only on the material itself and factors like temperature, not on the object's shape or size. Understanding the unit of resistivity is crucial in electrical calculations.
Deriving the Unit of Resistivity
The relationship between resistance ($R$), resistivity ($\rho$), length ($L$), and cross-sectional area ($A$) of a conductor is defined by the formula:
$R = \rho \frac{L}{A}$
To find the unit of resistivity ($\rho$), we can rearrange this formula:
$\rho = \frac{R \times A}{L}$
Determining the Units
Let's look at the standard units for each term in the rearranged formula:
- The unit of Resistance ($R$) is the Ohm, symbolized as ($\Omega$).
- The unit of Length ($L$) is the metre, symbolized as ($m$).
- The unit of Area ($A$) is the square metre, symbolized as ($m^2$).
Calculating Resistivity's Unit
Now, substitute these units back into the formula for resistivity:
Unit of $\rho = \frac{\text{Unit of } R \times \text{Unit of } A}{\text{Unit of } L}$
Unit of $\rho = \frac{\Omega \times m^2}{m}$
Simplifying the expression by canceling out one metre ($m$):
Unit of $\rho = \Omega \cdot m$
Therefore, the unit of resistivity is Ohm metre.
Evaluating the Options
Based on our derivation, let's examine the given options:
- mho: This is the unit of conductance, the reciprocal of resistance.
- ohm metre: This matches our calculated unit for resistivity.
- mho metre: This is an incorrect unit combination.
- ohm: This is the unit of resistance, not resistivity.
The correct unit for resistivity is Ohm metre ($\Omega \cdot m$).
