Question

The resistance of a wire depends directly on the length of the wire and inversely as the cross-sectional area of the wire. If both the length and the diameter of the wire are halved, the percentage change in the resistance of the wire will be:

• A. $0\%$
• B. $50\%$
• C. $100\%$
• D. $200\%$

Answer 1

Answer: (C)

$100\%$

Let the given Function be represented as

$Resistance=k(\frac{length}{Area})$

when we halve the $length$ and $Diameter$ Area will be Divided by $4$ as $A$ is proportional to $square$ of $radius/Diameter$

Now,New Resistance

$Resistanc{e}_1=k(\frac{length/2}{Area/4})$

$Resistanc{e}_1=2k(\frac{length}{Area})$

Since it is $Double$ the given function,The percentage change in the resistance of the wire will be $100$%.

Therefore Answer is $\left(C\right)$