Question

Units for specific resistance

• A. \(\Omega \cdot m\)
• B. \(\Omega/ m\)
• C. \(m/ \Omega\)
• D. \(\Omega kg \)

Answer 1

The Correct Option is A

To determine the correct units for specific resistance, let's analyze the concept step by step.

1. Understanding Specific Resistance:
Specific resistance (also known as resistivity) is a material property that quantifies how strongly a material opposes the flow of electric current. It is denoted by the symbol $\rho$ (rho).

The formula for resistivity is given by:
$$ \rho = \frac{R \cdot A}{L} $$ where:

• $R$ is the resistance of the material (in ohms, $\Omega$),
• $A$ is the cross-sectional area of the material (in square meters, $m^2$),
• $L$ is the length of the material (in meters, $m$).

 

2. Deriving the Units:
From the formula $\rho = \frac{R \cdot A}{L}$, we can substitute the units of each quantity:

• $R$ has units of $\Omega$,
• $A$ has units of $m^2$,
• $L$ has units of $m$.

Thus, the units of $\rho$ are: $$ \text{Units of } \rho = \frac{\text{Units of } R \cdot \text{Units of } A}{\text{Units of } L} = \frac{\Omega \cdot m^2}{m} $$ Simplifying the expression: $$ \frac{\Omega \cdot m^2}{m} = \Omega \cdot m $$

Final Answer: $ {(A) \, \Omega \cdot m} $