મીટરબ્રિજના પ્રયોગ માટેનો પરિપથ નીચેની આકૃતિમાં આપેલ છે.શરૂઆતમાં અવરોધ \(P\, = 4\,\Omega \) અને તટસ્થ બિંદુ \(N\) \(A\) થી \(60\,cm\) અંતરે મળે છે.હવે એક \(R\) અવરોધને \(P\) સાથે શ્રેણીમાં જોડવામાં આવે તો તટસ્થ બિંદુ \(N\) \(A\) થી \(80\,cm\) અંતરે મળે છે. તો અવરોધ \(R\) નું મૂલ્ય કેટલું હશે?

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.

Same subject

Explore more questions on app

From JEE Mains

Explore more questions on app