બેટરી (કોષ) નો આંતરિક અવરોધ માપવા માટે પોટેન્શીયોમીટરનો ઉપયોગ કરવામાં આવે છે. \(R=10 \Omega\) માટે તટસ્થ (સંતુલન) બિંદુ \(l=500 \mathrm{~cm}\) અંતરે અને \(R=1 \Omega\) માટે તટસ્થ બિંદુ \(l=400 \mathrm{~cm}\) આગળ મળે છે. બેટરીનાં આંતરિક અવરોધનું આશરે મૂલ્ય _______ થશે.

A \(0.2 \Omega\)
B \(0.4 \Omega\)
C \(0.1 \Omega\)
D \(0.3 \Omega\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(0.3 \Omega\)

Step-by-step Solution

Detailed explanation

Let potential gradient be \(\lambda\). \(\therefore \mathrm{i} \times 10=\lambda \times 500=\varepsilon-\mathrm{ir}_{\mathrm{s}}\) \(\Rightarrow 500 \lambda=\varepsilon-50 \lambda \mathrm{r}_{\mathrm{s}}\) Also,…

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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