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Question
State whether the following statement is True or False.
A wire is stretched to double its length. Then its resistance become four times.
True or False
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Solution
This statement is true.
Explanation:
When a wire is stretched to double its original length, its volume remains constant, assuming uniform stretching.
Since,
\[ V = AL \]
\[ A'L' = AL \]
Given \(L' = 2L\),
\[ A' = \frac{A}{2} \]
We know that,
\[ R=\rho\frac{L}{A} \]
Therefore, the new resistance is
\[ R' =\rho\frac{2L}{A/2} \]
\[ R' =4\rho\frac{L}{A} \]
\[ {R' = 4R}\]
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Chapter 4: Electricity and Magnetism - Graded Assignment 4.2 [Page 253]
