What is unit for resistivity of a metal ?

Options

A. `ohm`
B. `ohm cm ^(-1)`
C. `ohm cm ^(-2)`
D. `ohm cm `

Answer

To find the unit for resistivity of a metal, we can start from the formula that relates resistivity to resistance, length, and cross-sectional area.

### Step-by-Step Solution:

1. **Understand the Formula for Resistivity**:
The resistivity (ρ) of a material is defined by the formula:
\[ \rho = R \times \frac{A}{L} \]
where:
- \( \rho \) = resistivity (in ohm-meters, Ω·m)
- \( R \) = resistance (in ohms, Ω)
- \( A \) = cross-sectional area (in square meters, m²)
- \( L \) = length of the conductor (in meters, m)

2. **Identify the Units**:
- The unit of resistance \( R \) is ohms (Ω).
- The unit of cross-sectional area \( A \) is square meters (m²).
- The unit of length \( L \) is meters (m).

3. **Substitute the Units into the Formula**:
Rearranging the formula for resistivity, we can express it in terms of its units:
\[ \rho = R \times \frac{A}{L} \]
Substituting the units:
\[ \rho = \Omega \times \frac{m²}{m} \]

4. **Simplify the Units**:
Simplifying the right side:
\[ \rho = \Omega \times m = \Omega \cdot m \]

5. **Conclusion**:
Therefore, the unit for resistivity of a metal is:
\[ \text{Resistivity} = \Omega \cdot m \]

### Final Answer:
The unit for resistivity of a metal is ohm-meter (Ω·m).

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