• # question_answer There identical capacities ${{C}_{1}},{{C}_{2}}$ and ${{C}_{3}}$ of capacitance $6\mu F,$ each one is connected to a 12 V battery as shown in figure. (i) Charge on each capacitor (ii) Equivalent capacitance of the network (iii) Energy stored in the network of capacitor

(i) Capacitors ${{C}_{1}}$ and ${{C}_{2}}$ are in series across the 12 V supply. Equivalent capacitance of ${{C}_{1}}$ and ${{C}_{2}},$ ${{C}_{eq}}=\frac{{{C}_{1}}\,{{C}_{2}}}{{{C}_{2}}+{{C}_{2}}}$ ${{C}_{eq}}=\frac{6\times 6}{6+6}=3\mu F$ Charges of ${{C}_{1}}$ and ${{C}_{2}}$ are equal as they are in series, ${{q}_{1}}={{q}_{2}}={{C}_{eq}}V=3\mu F\times 12=36\times {{10}^{-6}}C=36\mu C$ Charge on capacitor ${{C}_{3}},{{q}_{3}}={{C}_{3}}V$             $=6\mu F\times 12=72\mu F$ (ii) Equivalent capacitance of the network, ${{C}_{eff}}={{C}_{eq}}+C=3+6=9\mu F$ (iii) Energy stored in the network $=\frac{1}{2}{{C}_{eff}}{{V}^{2}}=\frac{1}{2}\times 9\times {{10}^{-6}}\times {{12}^{2}}$             $=6.48\times {{10}^{-4}}\,J$
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