CBSE Class 10 Science 2018 · Paper 31/1/C · Question 12(b)

Electrical resistivity: The resistance of a uniform conductor is $R=\rho \frac{l}{A}$, where $l$ is its length and $A$ its area of cross-section; the constant $\rho$ is the electrical resistivity of its material. It equals the resistance of a conductor of that material of unit length ($1$ m) and unit area of cross-section ($1{\text{m}}^2$). It depends on the nature of the material (and on temperature), not on the length or thickness of the conductor. SI unit: $\rho =\frac{RA}{l}$, so its unit is $\frac{\Omega \times {\text{m}}^2}{\text{m}}=\Omega$ m (ohm metre). Current: The current becomes half, i.e. $50$ mA. Justification: for the same material and thickness $R\propto l$, so doubling the length doubles the resistance, $R^{\prime }=2R$. The battery voltage $V$ is unchanged, so by Ohm's law $I^{\prime }=\frac{V}{2R}=\frac{I}{2}=\frac{100\text{mA}}{2}=50$ mA.