A condenser of capacity ' $\mathrm{C}_1$ ' is charged to potential ' $\mathrm{V}_1$ ' and then disconnected.…

A condenser of capacity ' $\mathrm{C}_1$ ' is charged to potential ' $\mathrm{V}_1$ ' and then disconnected. Uncharged capacitor of capacity ' $\mathrm{C}_2$ ' is connected in parallel with ' $\mathrm{C}_1$ '. The resultant potential ' $\mathrm{V}_2$ ' is
  1. $\frac{\mathrm{V}_1 \mathrm{C}_2}{\mathrm{C}_1}$
  2. $\frac{\mathrm{C}_2}{\mathrm{C}_1+\mathrm{C}_2}$
  3. $\frac{\mathrm{C}_1 \mathrm{~V}_1}{\mathrm{C}_2}$
  4. $\frac{\mathrm{C}_1 \mathrm{~V}_1}{\mathrm{C}_1+\mathrm{C}_2}$

Solution

The charge stored by the charged condenser is $\mathrm{Q}=\mathrm{C}_1 \mathrm{~V}_1$ When the uncharged condenser is connected in parallel, the effective capacitance becomes $\left(\mathrm{C}_1+\mathrm{C}_2\right)$ Hence the potential, $\mathrm{V}_2=\frac{\mathrm{Q}}{\mathrm{C}_1+\mathrm{C}_2}=\frac{\mathrm{C}_1 \mathrm{~V}_1}{\mathrm{C}_1+\mathrm{C}_2}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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