આપેલ મીટરબ્રિજના પરિપથમાં \(Y=12.5\, \Omega \) અને જૉકી \(J\) દ્વારા \(A\) બાજુથી \(39.5\, cm\) અંતરે તટસ્થ બિંદુ મળે છે. \(X\) અને \(Y\) અવરોધોની અદલાબદલી કરા પછી નવું તટસ્થ બિંદુ \(A\) બાજુથી \(l_2\) અંતરે મળતું હોય તો \(X\) અને \(l_2\) નું મૂલ્ય કેટલુ હશે?

A \(19.15\,\Omega \) અને \(39.5\,cm\)
B \(8.16\,\Omega \) અને \(60.5\,cm\)
C \(19.15\,\Omega \) અને \(60.5\,cm\)
D \(8.16\,\Omega \) અને \(39.5\,cm\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(8.16\,\Omega \) અને \(60.5\,cm\)

Step-by-step Solution

Detailed explanation

For a balanced meter bridge, \(\frac{X}{39.5}=\frac{Y}{(100-39.5)}\) \(\Rightarrow Y=39.5=X \times(100-39.5)\) or, \(\quad {\rm{X}} = \frac{{12.5 \times 39.5}}{{60.5}} = 8.16\,\Omega \) \({\text { When } X \text { and } Y \text { are interchanged } l_{1} \text { and }(100} \)…

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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