Resistivity, ammeter reading and wire resistance

Electrical resistivity ($ho$) is a fundamental property of a material defined as the resistance offered by a conductor of unit length and unit cross-sectional area. Its SI unit is $\Omega\cdot\text{m}$.

1. Resistance $R \propto l$. If length becomes $3l$, new resistance $R' = 3R$.
2. Since current $I = \frac{V}{R}$, $I' = \frac{V}{3R} = \frac{I}{3}$.
3. New current reading = $\frac{300\text{ mA}}{3} = 100\text{ mA}$.

Using formula $R = \rho \frac{l}{A}$: Given:

• $l = 500\text{ m}$
• $A = 1 \times 10^{-3}\text{ m}^2$
• $\rho = 2.65 \times 10^{-8}\ \Omega\text{ m}$

$R = \frac{2.65 \times 10^{-8} \times 500}{1 \times 10^{-3}} = \frac{1325 \times 10^{-8}}{10^{-3}} = 1.325 \times 10^{-2}\ \Omega = 0.01325\ \Omega$