આકૃતિમાં દર્શાવ્યા મુજબ બે અવરોધો \( R_{1} \) અને \( R_{2} \) સાથેનો એક મીટર બ્રિજ બિંદુ P થી 40 cm અંતરે સંતુલિત (શૂન્ય બિંદુ) હતો. જ્યારે 16 \( \Omega \) અવરોધને \( R_{2} \) ને સમાંતર જોડવામાં આવે છે, ત્યારે શૂન્ય બિંદુ બિંદુ P થી 50 cm અંતરે બદલાઈ ગયું. અવરોધો \( R_{1} \) અને \( R_{2} \) ના મૂલ્યો __________ છે.

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.

Same subject

Explore more questions on app

From JEE Mains

Explore more questions on app