આકૃતિમાં દર્શાવ્યા અનુસાર અવરોધોને મીટર બ્રીજમાં જોડવામાં આવ્યા છે. સંતોલન લંબાઈ \(l_1\) એ \(40\,cm\) છે. હવે અજ્ઞાત અવરોધ \(x\) ને \(P\) સાથે શ્રેણીમાં જોવામાં આવે છે અને નવું સંતોલન બિંદુ, તે જ છેડા થી, \(80\,cm\) જેટલું મળે છે. \(x\) નું મૂલ્ય \(............\Omega\) હશે.

A \(2.2\)
B \(22\)
C \(200\)
D \(20\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(20\)

Step-by-step Solution

Detailed explanation

Initially, \(\frac{ P }{ Q }=\frac{40 cm }{60 cm }=\frac{2}{3}\) Finally, \(\frac{ P + x }{ Q }=\frac{80 cm }{20 cm }=\frac{4}{1} \ldots(2)\) Divide \((2)\) by \((1)\) \(\frac{ P + x }{ P }=4 \times \frac{3}{2}=6\) \(1+\frac{ x }{ P }=6 \Rightarrow \frac{ x }{ P }=5\)…

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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