The length of a metallic wire is increased by $20 \%$ and its area of cross section is reduced by $4 \%$. The percentage change in resistance of the metallic wire is __________.
Answer (integer)
25
Solution
<p>The resistance ($R$) of a wire can be calculated by the formula:</p>
<p>$ R = \rho \frac{L}{A}, $</p>
<p>where</p>
<ul>
<li>$\rho$ is the resistivity (a property of the material),</li>
<li>$L$ is the length of the wire, and</li>
<li>$A$ is the cross-sectional area of the wire.</li>
</ul>
<p>If the length ($L$) is increased by 20%, $L$ becomes $1.2L$.<br/><br/> If the cross-sectional area ($A$) is reduced by 4%, $A$ becomes $0.96A$.</p>
<p>The new resistance $R'$ is then:</p>
<p>$ R' = \rho \frac{1.2L}{0.96A} = 1.25R, $</p>
<p>so the resistance has increased by 25%.</p>
<p>Therefore, the percentage change in the resistance of the metallic wire is 25%.</p>
About this question
Subject: Physics · Chapter: Current Electricity · Topic: Ohm's Law and Resistance
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