Question

The electrical resistivity of silver is $1.60\times {10}^{-6}\Omega m$. What will be the resistance of a silver wire of length $10m$ and cross-sectional area $2\times {10}^{-3}{m}^2$?

Answer 1

Step 1- Given data and formula

1. Length of the silver wire $l=10m$
2. Area of cross-section $A=2\times {10}^{-3}{m}^2$
3. Resistivity of silver $\rho =1.60\times {10}^{-6}\Omega m$

The formula for resistance $R$ is

$R=\rho \frac{l}{A}$

Step 2- Finding the resistance of the silver wire

Substitute the values into the above formula to calculate $R$.

$$\begin{gathered} R=(1.60\times {10}^{-6}\Omega m)\times \frac{(10m)}{(2\times {10}^{-3}{m}^2)} \\ R=8\times {10}^{-3}\Omega \end{gathered}$$

Hence, the resistance of the silver wire is $8\times {10}^{-3}\Omega$.