MHTCET 13 Apr 2026 Shift 1 Paper

Concept:In a series combination of capacitors, the charge on every capacitor is the same, while the total e.m.f. of the battery is divided across them.Explanation:Let the capacitance of each identical air capacitor be $C$.When one capacitor is immersed in a liquid of dielectric constant $K$, its capacitance becomes $KC$.The other capacitor remains an air capacitor with capacitance $C$.For the series combination, the equivalent capacitance is:$$C_{\mathrm{eq}} = \frac{KC \cdot C}{KC + C} = \frac{KC}{K+1}$$The total charge supplied by the battery is:$$Q = C_{\mathrm{eq}}V = \frac{KC V}{K+1}$$In series, the same charge $Q$ flows through both capacitors.Hence, the potential difference across the other capacitor of capacitance $C$ is:$$V_{\text{other}} = \frac{Q}{C} = \frac{\frac{KC V}{K+1}}{C} = \frac{K V}{K+1}$$Thus, the potential difference of the other capacitor depends only on $K$ and $V$.Answer:The potential difference of the other capacitor becomes $\frac{K V}{K+1}$, so the correct option is A.