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 \[\frac{1}{2}\frac{{{C}_{1}}}{{{n}_{1}}}{{(4V)}^{2}}=\frac{1}{2}({{n}_{2}}{{C}_{2}}){{V}^{2}}\] \[\Rightarrow \] \[{{C}^{2}}=\frac{16{{C}_{1}}}{{{n}_{2}}\,{{n}_{1}}}\]

"> 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 \[\frac{1}{2}\frac{{{C}_{1}}}{{{n}_{1}}}{{(4V)}^{2}}=\frac{1}{2}({{n}_{2}}{{C}_{2}}){{V}^{2}}\] \[\Rightarrow \] \[{{C}^{2}}=\frac{16{{C}_{1}}}{{{n}_{2}}\,{{n}_{1}}}\]

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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]

NEET Physics in NEET 1 year ago

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[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 \[\frac{1}{2}\frac{{{C}_{1}}}{{{n}_{1}}}{{(4V)}^{2}}=\frac{1}{2}({{n}_{2}}{{C}_{2}}){{V}^{2}}\] \[\Rightarrow \] \[{{C}^{2}}=\frac{16{{C}_{1}}}{{{n}_{2}}\,{{n}_{1}}}\]

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