A wire of 3 $Ω$ resistance and 10 cm length is stretched to 30 cm length. Assuming that it has uniform cross-section, what will be its new resistance?

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Solution

Original resistance = $R_{o} = ρ \times \frac{I}{A}$
The resistance of conductor is directly proportional to its length and inversely proportional to its cross sectional area.
The wire tripled of its previous length so the length will be $3 l$
And the new cross sectional area will be $\frac{A}{3}$
$R_{n} = 3 \times ρ \times \frac{l}{A / 3}$
= $9 R = 9 ρ \times \frac{l}{A}$
= $9 \times 3 = 27$ ohm

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iii) Resistivity.

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