A $10\,\mu F$ capacitor and a $20\,\mu F$ capacitor are connected in series across a $200\;V$ supply line. The charged capacitors are then disconnected from the line and reconnected with their positive plates together and negative plates together and no external voltage is applied. What is the potential difference across each capacitor
Medium
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(b) Initially potential difference a cross each capacitor
${V_1} = \frac{{20}}{{(10 + 20)}} \times 200 = \frac{{400}}{3}\,V$
and ${V_2} = \frac{{10}}{{(10 + 20)}} \times 200 = \frac{{200}}{3}\,V$
Finally common potential $V = \frac{{{C_1}{V_1} + {C_2}{V_2}}}{{{C_1} + {C_2}}}$
$V = \frac{{10 \times \frac{{400}}{3} + 20 \times \frac{{200}}{3}}}{{(10 + 20)}} = \frac{{800}}{9}\,V$
${V_1} = \frac{{20}}{{(10 + 20)}} \times 200 = \frac{{400}}{3}\,V$
and ${V_2} = \frac{{10}}{{(10 + 20)}} \times 200 = \frac{{200}}{3}\,V$
Finally common potential $V = \frac{{{C_1}{V_1} + {C_2}{V_2}}}{{{C_1} + {C_2}}}$
$V = \frac{{10 \times \frac{{400}}{3} + 20 \times \frac{{200}}{3}}}{{(10 + 20)}} = \frac{{800}}{9}\,V$
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