MHT CET · Physics · Current Electricity

A conducting wire has length \(L_1\) and diameter \(d_1\). After stretching the same wire length becomes \(L_2\) and diameter \(d_2\). The ratio of resistance before and after strectching is

A \(d_2^4: d_1^4\)
B \(d_1^4: d_2^4\)
C \(d_{2}^{2}:d_{1}^{2}\)
D \(d_1^2: d_2^2\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(d_2^4: d_1^4\)

Step-by-step Solution

Detailed explanation

\(\frac{R_1}{R_2}=\frac{L_1}{L_2} \times \frac{A_2}{A_1}=\frac{L_1}{L_2} \times \frac{\frac{\pi d 22}{4}}{\frac{\pi d_1^2}{4}}\quad\ldots(1)\)
\(L_1 d_1^2=L_2 d_2^2\quad\ldots(2)\)
\(\frac{L_1}{L_2}=\left(\frac{d_2}{d_1}\right)^2\)
\(\frac{R_1}{R_2}=\left(\frac{L_1}{L_2}\right) \times\left(\frac{d_2}{d_1}\right)^2\)
\(=\frac{d_2^4}{d_1^4}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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