• # question_answer A series combination of n1 capacitors, each of value ${{C}_{1}},$ is charged by a source of potential difference 4V. When another parallel combination of ${{n}_{2}}$ capacitors, each of value ${{C}_{2}},$ is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of ${{C}_{2}},$ in terms of ${{C}_{1}},$ is then                      [AIPMT (S) 2010] A) $\frac{2{{C}_{1}}}{{{n}_{1}}\,{{n}_{2}}}$ B) $16\frac{{{n}_{2}}}{{{n}_{1}}\,}{{C}_{1}}$ C) $2\frac{{{n}_{2}}}{{{n}_{1}}\,}{{C}_{1}}$ D) $\frac{16{{C}_{1}}}{{{n}_{1}}\,{{n}_{2}}\,}$

 [d] Case I. When the capacitors are joined in series ${{U}_{series}}=\frac{1}{2}\frac{{{C}_{1}}}{{{n}_{1}}}{{(4V)}^{2}}$ Case II. When the capacitors are joined in parallel ${{U}_{parallel}}=\frac{1}{2}({{n}_{2}}{{C}_{2}}){{V}^{2}}$ Given, ${{U}_{series}}={{U}_{parallel}}$ or         $\frac{1}{2}\frac{{{C}_{1}}}{{{n}_{1}}}{{(4V)}^{2}}=\frac{1}{2}({{n}_{2}}{{C}_{2}}){{V}^{2}}$ $\Rightarrow$   ${{C}^{2}}=\frac{16{{C}_{1}}}{{{n}_{2}}\,{{n}_{1}}}$