The S.I. unit of resistivity is

Options

A. `Omega`
B. `Omega-m`
C. `m`
D. A

Answer

To determine the S.I. unit of resistivity, we can follow these steps:

### Step 1: Understand the concept of resistivity
Resistivity is a property of a material that quantifies how strongly it resists the flow of electric current. It is denoted by the symbol ρ (rho).

### Step 2: Recall the relationship between resistance, resistivity, length, and area
The resistance (R) of a conductor can be expressed in terms of its resistivity (ρ), length (L), and cross-sectional area (A) using the formula:
\[ R = \frac{\rho L}{A} \]

### Step 3: Rearrange the formula to express resistivity
From the formula above, we can rearrange it to find the expression for resistivity:
\[ \rho = R \cdot \frac{A}{L} \]

### Step 4: Identify the units involved
- The unit of resistance (R) is ohm (Ω).
- The unit of area (A) is square meters (m²).
- The unit of length (L) is meters (m).

### Step 5: Substitute the units into the resistivity formula
Substituting the units into the rearranged formula for resistivity gives:
\[ \text{Unit of } \rho = \text{Unit of } R \cdot \frac{\text{Unit of } A}{\text{Unit of } L} \]
\[ \text{Unit of } \rho = \Omega \cdot \frac{m^2}{m} \]

### Step 6: Simplify the units
When we simplify the units:
\[ \text{Unit of } \rho = \Omega \cdot m \]
Thus, the S.I. unit of resistivity is ohm-meter (Ω·m).

### Conclusion
The S.I. unit of resistivity is **ohm-meter (Ω·m)**.

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