A student is given four identical batteries having emf 1.5 V each and internal resistance of \(0.1 \Omega\) each. The student is asked to connect them in assisting manner. By mistake he connect one battery in reverse way. The resultant \(e m f\) and resultant internal resistance offered by the combination is _________.

A \(3 V, 0.4 \Omega\)
B \(4.5 \vee 0.3 \Omega\)
C \(3 V, 0.2 \Omega\)
D \(6.0 V, 0.4 \Omega\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(3 V, 0.4 \Omega\)

Step-by-step Solution

Detailed explanation

A
equivalent \(e m f\) in assisting manner
\(\begin{array}{l}\varepsilon^{\prime}=\varepsilon+\varepsilon+\varepsilon-\varepsilon \\ \varepsilon^{\prime}=2 \varepsilon \\ \varepsilon^{\prime}=2 \times 1.5 \\ \varepsilon^{\prime}=3 V\end{array}\)
equivalent internal resistance
\(\begin{array}{l}r^{\prime}=r+r+r+r \\ r^{\prime}=4 r \\ r^{\prime}=4 \times 0.1 \\ r^{\prime}=0.4 \Omega\end{array}\)

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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