JEE Mains · Physics · STD 12 - 3. current electricity
A \(1\,m\) long wire is broken into two unequal parts \(X\) and \(Y\) The \(X\) part of the wire is streched into another wire \(W\). Length of \(W\) is twice the length of \(X\) and the resistance of \(W\) is twice that of \(Y\). Find the ratio of length of \(X\) and \(Y\).
- A \(1: 4\)
- B \(1: 2\)
- C \(4: 1\)
- D \(2: 1\)
Answer & Solution
Correct Answer
(B) \(1: 2\)
Step-by-step Solution
Detailed explanation
\(\frac{ R _{ X }}{ R _{ Y }}=\frac{\ell_{ X }}{\ell_{ Y }}\) When wire is stretched to double of its length, then resistance becomes 4 times \(R _{ W }=4 R _{ X }=2 R _{ Y }\) \(\frac{ R _{ X }}{ R _{ Y }}=\frac{1}{2}\) So. \(\frac{\ell_{ X }}{\ell_{ y }}=\frac{1}{2}\)
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