આપેલ આકૃતિમાં, પોટેન્શિયોમીટરના તાર ની લંબાઈ \(A B=10 \,{m}\) છે. પ્રતિ એકમ લંબાઈ દીઠ અવરોધ \(0.1 \,\Omega/cm\) છે. \({AB}\) ને \(E\;emf\) અને \(r\) આંતરિક અવરોધ \(r\) ની બેટરી સાથે જોડેલ છે. આ પોટેન્શિયોમીટર દ્વારા માપવામાં આવેલ \(emf\) નું મહત્તમ મૂલ્ય (\(V\) માં) કેટલું હશે?

A \(6\)
B \(2.25\)
C \(5\)
D \(2.75\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(5\)

Step-by-step Solution

Detailed explanation

Max. voltage that can be measured by this potentiometer will be equal to potential drop across AB \(R _{ AB }=10 \times 0.1 \times 100=100 \Omega\) \(\therefore V _{ AB }=\frac{6}{20+100} \times 100=6 \times \frac{100}{120}=5 V\)

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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