આપેલ આકૃતિમાં મીટરબ્રીજ \(AB\) નો અવરોધ \(4\,\Omega \) છે. \(\varepsilon \, = 0.5\,\,V\) જેટલું \(emf\) ધરાવતા કોષ અને \(R_h=2\,\Omega \) ધરાવતા રિહયોસ્ટેટ સાથે કોઇક બિંદુ \(J\) પાસે તટસ્થ બિંદુ મળે છે. જ્યારે કોષને બીજા \(\varepsilon = \varepsilon_2\) જેટલા \(emf\) ધરાવતા કોષથી બદલવામાં આવે છે ત્યારે \(R_h=6\,\Omega \) માટે \(J\) બિંદુ આગળ જ તટસ્થ બિંદુ મળે છે \(\varepsilon_2\, emf\) .............. \(V\) થશે.

A \(0.4\)
B \(0.3\)
C \(0.6\)
D \(0.5\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(0.3\)

Step-by-step Solution

Detailed explanation

\(0.5=\frac{6}{(2+\lambda L)} \lambda x\) ......\((1)\) \(E_{2}=\frac{6}{(6+\lambda L)} \lambda x\) .......\((2)\) So dividing equation \(( 1)\) and \(( 2)\) \(\frac{E_{2}}{0.5}=\frac{2+4}{6+4}=\frac{3}{5}\) \(\Rightarrow \quad E_{2}=0.3\) \(volt\)

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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