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(B) battery is getting charged if the current enters through its positive terminal.Let the current from the $30\,V$ battery be $I_1$ and from the $15\

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$15\,V$

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(B) battery is getting charged if the current enters through its positive terminal.Let the current from the $30\,V$ battery be $I_1$ and from the $15\,V$ battery be $I_2$. Applying Kirchhoff's loop rule to the left loop $(ABCF)$: $30 - 4I_1 - 3(I_1 + I_2) - 2I_1 = 0 \Rightarrow 30 = 9I_1 + 3I_2 \Rightarrow 10 = 3I_1 + I_2$.Applying Kirchhoff's loop rule to the right loop $(FCDE)$: $15 - 1I_2 - 2I_2 - 3(I_1 + I_2) = 0 \Rightarrow 15 = 3I_1 + 6I_2 \Rightarrow 5 = I_1 + 2I_2$.Solving these equations: From the second,$I_1 = 5 - 2I_2$. Substituting into the first: $10 = 3(5 - 2I_2) + I_2 \Rightarrow 10 = 15 - 6I_2 + I_2 \Rightarrow 5I_2 = 5 \Rightarrow I_2 = 1\,A$.Then $I_1 = 5 - 2(1) = 3\,A$.Since $I_2$ flows out of the positive terminal of the $15\,V$ battery (as per our assumption),it is discharging. Let's re-examine the polarity. The $15\,V$ battery is connected such that the current $I_2$ flows into its positive terminal,meaning it is being charged.

The figure shows a network of five resistances and two batteries. Which of the batteries is getting charged?

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