Question

Calculate the resistivity of the material of a conductor of length 3 m, area of cross section \( 0.2 \, \text{mm}^2 \) having a resistance of 2 \( \Omega \).

Hint:

Resistivity is a material property that quantifies the material's opposition to electric current. It can be calculated using the formula \( \rho = \frac{R A}{L} \).

Answer 1

Step 1: Using the formula for resistance.
The resistance \( R \) of a conductor is related to the resistivity \( \rho \) by the formula: \[ R = \rho \frac{L}{A} \] where \( R = 2 \, \Omega \), \( L = 3 \, \text{m} \), and \( A = 0.2 \, \text{mm}^2 = 0.2 \times 10^{-6} \, \text{m}^2 \).
Step 2: Rearranging to find resistivity.
Rearranging the formula to solve for resistivity \( \rho \): \[ \rho = \frac{R A}{L} \] Substituting the known values: \[ \rho = \frac{2 \times (0.2 \times 10^{-6})}{3} \] \[ \rho = 1.33 \times 10^{-7} \, \Omega \cdot \text{m} \] Step 3: Conclusion.
Thus, the resistivity of the material is \( 1.33 \times 10^{-7} \, \Omega \cdot \text{m} \).