चित्र में दिखाए अनुसार $ R_{1} $ और $ R_{2} $ दो प्रतिरोधों वाले एक मीटर सेतु में बिंदु P से $40 cm$ की दूरी पर शून्य विक्षेप बिंदु प्राप्त होता है। जब 16 $ \Omega $ प्रतिरोध को $ R_{2} $ के समांतर क्रम में जोड़ा जाता है, तो शून्य विक्षेप बिंदु P बिंदु से 50 cm पर बदल जाता है। प्रतिरोधों $ R_{1} $ और $ R_{2} $ के मान __________ हैं।

A $ R_{2}=16\Omega, R_{1}=\frac{16}{3}\Omega $
B $ R_{2}=4\Omega, R_{1}=\frac{4}{3}\Omega $
C $ R_{2}=8\Omega, R_{1}=\frac{16}{3}\Omega $
D $ R_{2}=12\Omega, R_{1}=\frac{12}{3}\Omega $

Verified Solution

Answer & Solution

Correct Answer

(C) $ R_{2}=8\Omega, R_{1}=\frac{16}{3}\Omega $

Step-by-step Solution

Detailed explanation

$ \frac{R_{1}}{R_{2}}=\frac{40}{60}=\frac{2}{3} $ $\quad$... (1) $ \frac{R_{1}}{(\frac{R_{2}\times16}{R_{2}+16})}=\frac{50}{50}\Rightarrow R_{1}=\frac{16R_{2}}{16+R_{2}} $ $\quad$...(2) $ \frac{2}{3}R_{2}=\frac{16R_{2}}{16+R_{2}} $…

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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