\(10 \mathrm{~cm}\) લંબાઈ અને \(\sqrt{7} \times 10^{-4} \mathrm{~m}\) ત્રિજ્યા ના તારને મીટર બ્રીજના જમણા ગેપમાં જોડેલ છે.જ્યારે ડાબા ગેપમાં અવરોધ પેટી વડે \(4.5 \Omega\) નો અવરોધ જોડવામાં આવે ત્યારે ડાબા છેડેથી \(60 \mathrm{~cm}\) આગળ તટસ્થબિંદૂ (સંતુલન લંબાઈ) મળે છે.જો તારની અવરોધકતા \(\mathrm{R} \times 10^{-7} \Omega \mathrm{m}\) હોય તો \(\mathrm{R}\) નું મૂલ્ય_____છે.

A \(63\)
B \(70\)
C \(66\)
D \(35\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(66\)

Step-by-step Solution

Detailed explanation

For null point, \( \frac{4.5}{60}=\frac{R}{40} \) \( \text { Also, } R=\frac{\rho \ell}{A}=\frac{\rho \ell}{\pi r^2} \) \( 4.5 \times 40=\rho \times \frac{0.1}{\pi \times 7 \times 10^{-8}} \times 60 \) \( \rho=66 \times 10^{-7} \Omega \times \mathrm{m}\)

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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