Question

a given wire of resistance 10 ohms as a length of 5 m and a cross-sectional area of 4.0 * 10 ^ -3 m calculate the conductivity of The Wire

Answer 1

To calculate the conductivity of the wire, we can use the formula that relates conductivity (\( \sigma \)), resistivity (\( \rho \)), and resistance (\( R \)). The resistivity is given by the equation:

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

where:
- \( R \) is the resistance (in ohms),
- \( \rho \) is the resistivity (in ohm-meters),
- \( L \) is the length of the wire (in meters), and
- \( A \) is the cross-sectional area of the wire (in square meters).

Rearranging the equation to find resistivity:

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

Now we can substitute the known values into the equation:
- \( R = 10 \, \Omega \)
- \( L = 5 \, m \)
- \( A = 4.0 \times 10^{-3} \, m^2 \)

\[
\rho = 10 \, \Omega \times \frac{4.0 \times 10^{-3} \, m^2}{5 \, m}
\]

Calculating \( \rho \):

\[
\rho = 10 \times \frac{4.0 \times 10^{-3}}{5} = 10 \times 0.0008 = 0.008 \, \Omega \cdot m
\]

Next, we find the conductivity (\( \sigma \)), which is the reciprocal of resistivity:

\[
\sigma = \frac{1}{\rho}
\]

\[
\sigma = \frac{1}{0.008 \, \Omega \cdot m} = 125 \, S/m
\]

Therefore, the conductivity of the wire is \( \sigma = 125 \, S/m \).