Calculate the area of cross-section of a wire if its length is `.0 m`, its resistance is `23 Omega` and the resistivity of the material is `1.84 xx 10^-6 Omega m`.

Explanation

To calculate the area of cross-section of a wire, we can use the formula that relates resistance (R), resistivity (ρ), length (L), and area (A):

\[ R = \frac{\rho L}{A} \]

Where:
- \( R \) is the resistance of the wire (in ohms, Ω)
- \( \rho \) is the resistivity of the material (in ohm-meters, Ω·m)
- \( L \) is the length of the wire (in meters, m)
- \( A \) is the area of cross-section of the wire (in square meters, m²)

We can rearrange this formula to solve for the area \( A \):

\[ A = \frac{\rho L}{R} \]

Now, let's substitute the given values into the equation:

- Length \( L = 1.0 \, \text{m} \)
- Resistance \( R = 23 \, \Omega \)
- Resistivity \( \rho = 1.84 \times 10^{-6} \, \Omega \cdot \text{m} \)

Substituting these values into the formula:

\[ A = \frac{(1.84 \times 10^{-6} \, \Omega \cdot \text{m}) \times (1.0 \, \text{m})}{23 \, \Omega} \]

Calculating the numerator:

\[ 1.84 \times 10^{-6} \, \Omega \cdot \text{m} \times 1.0 \, \text{m} = 1.84 \times 10^{-6} \, \Omega \cdot \text{m}^2 \]

Now, dividing by the resistance:

\[ A = \frac{1.84 \times 10^{-6} \, \Omega \cdot \text{m}^2}{23 \, \Omega} \]

Calculating the area:

\[ A = 8.00 \times 10^{-8} \, \text{m}^2 \]

Thus, the area of cross-section of the wire is:

\[ \boxed{8.00 \times 10^{-8} \, \text{m}^2} \]