A) \[\frac{{{V}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}}{{{V}_{1}}+{{V}_{2}}}\]
B) \[\frac{{{C}_{1}}{{V}_{1}}^{2}+{{C}_{2}}{{V}_{2}}^{2}}{{{V}_{1}}^{2}+{{V}_{2}}^{2}}\]
C) \[{{C}_{1}}+{{C}_{2}}\]
D) \[\frac{{{C}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}^{2}}{{{C}_{1}}+{{C}_{2}}}\]
Correct Answer: D
Solution :
When two conductors of capacities \[{{C}_{1}}\]and \[{{C}_{2}}\] and potentials\[{{V}_{1}}\] and \[{{V}_{2}}\]are connected by a conducting wire, charge redistributes in these conductors till potential of both the conductors become equal, known as common potential. Common potential \[=\frac{\text{net}\,\text{charge}}{\text{total}\,\text{capacity}}\] i.e., \[V=\frac{{{q}_{1}}+{{q}_{2}}}{{{C}_{1}}+{{C}_{2}}}\] or \[V=\frac{{{C}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}}{{{C}_{1}}+{{C}_{2}}}\]
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