In a series electrical circuit comprising

Question:

In a series electrical circuit comprising a resistor made up of a metallic wire, the ammeter reads 5A. The reading of ammeter decreases to half when the length of the wire is doubled. Why ?

Solution:

Resistance of wire length $l, \mathrm{R}=\frac{\rho l}{\mathrm{~A}}$.

When length becomes double, $\mathrm{R}^{\prime}=\frac{2 \rho l}{\mathrm{~A}}$.

$\therefore \quad \frac{\mathrm{R}^{\prime}}{\mathrm{R}}=2 \quad$ or $\quad \mathrm{R}^{\prime}=2 \mathrm{R}$

$I=\frac{V}{R} \quad$ and $I^{\prime}=\frac{V}{R^{\prime}}$

Since $V$ is same in both cases.

$\therefore \quad \frac{\mathrm{I}^{\prime}}{\mathrm{I}}=\frac{\mathrm{R}^{\prime}}{\mathrm{R}}=\frac{1}{2} \quad$ or $\quad \mathrm{I}^{\prime}=\frac{\mathrm{I}}{2}$

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