किसी मीटर सेतु प्रयोग के दौरान, प्रतिरोधों को चित्रानुसार जोड़ा गया है। शुरू में प्रतिरोध \(P =4 \Omega\) तथा नल बिन्दु \(N\), बिन्दु \(A\) से, \(60\; cm\) की दूरी पर है। एक अज्ञात प्रतिरोध \(R\) को \(P\) के साथ श्रेणी क्रम में जोड़ा जाता है जिससे नल बिन्दु की नई स्थिति बिंदु \(A\) से \(80\; cm\) दूर हो जाती है। अज्ञात प्रतिरोध \(R\) का मान होगा

A \(\frac{33}{5}\, \Omega \)
B \( 6\,\Omega \)
C \( 7\,\Omega \)
D \(\frac{20}{3}\, \Omega \)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{20}{3}\, \Omega \)

Step-by-step Solution

Detailed explanation

In balance position of bridge, \(\frac{P}{Q}=\frac{l}{(100-l)}\) Initially neutral position is \(60\, \mathrm{cm} .\) from \(\mathrm{A}\), so \(\frac{4}{60}=\frac{Q}{40} \Rightarrow Q=\frac{16}{6}=\frac{8}{3}\, \Omega\) Now, when unknown resistance \(\mathrm{R}\) is connected in…

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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