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I learnt that for an uncharged capacitor of capacitance $C$ connected with battery voltage $V$, the energy stored by capacitor is equal to $\frac{1}{2}CV^2$. But in this example for the capacitor connected in parallel with the circuit on the right, will it get the same energy as the other capacitor connected on the left ( since the voltage drop across them cannot be equal). Even observation is taken for a long time, the left capacitor will accumulate charge and develop voltage as that of the battery across it and disconnect the left part of the circuit before the right one does the same. Is my opinion true? If not plz tell me the right concept.

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After a long time both capacitors look like open circuits. That means there is no current flowing anywhere in the circuit. Like you stated all the battery voltage is across the left capacitor. Since no current is flowing in the resistor in parallel with the series combination of the right capacitor and its resistor, there is no voltage across them. The voltage across the right capacitor has to be zero and there is no energy stored in it.

Hope this helps

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