question_answer

Two condenses of capacity 0.3uF and 0.6uF respectively are connected in series. The combination is connected across a potential of 6V. The ratio of energies stored by the condenser will be:

A) \[\frac{1}{2}\]                          

B) 2     

C) \[\frac{1}{4}\]                          

D) 4

Correct Answer: B

Solution :

In series voltage is divided in inverse ratio of capacitance \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{{{C}_{2}}}{{{C}_{1}}}=\frac{0.6}{0.3}=\frac{2}{1}\] \[{{\operatorname{E}}_{1}}=\frac{1}{2}\times {{C}_{1}}{{V}_{1}}^{2}=\frac{1}{2}\times 0.3\mu F\times {{V}_{1}}^{2}\] \[{{\operatorname{E}}_{2}}=\frac{1}{2}\times {{C}_{2}}{{V}_{2}}^{2}=\frac{1}{2}\times 0.6\mu F\times {{V}_{2}}^{2}\] \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{2}{1}\]