Question

Two condensers, one of capacity C and other of capacity $\frac{C}{2}$ are connected to a V volt battery, as shown in the figure. The work done in charging fully both the condensers is:

• A. $\frac{1}{4}{CV}^2$
• B. $\frac{3}{4}{CV}^2$
• C. $\frac{1}{2}{CV}^2$
• D. $2{CV}^2$

Answer 1

The correct option is B $\frac{3}{4}{CV}^2$

$Q_1=CVand{Q}_2=\frac{CV}{2}$

Energy stored in capacitprs $=\frac{Q_1^2}{2C}+\frac{Q_2^2}{2\times 5}=\frac{C^2{V}^2}{2C}+\frac{C^2{V}^2}{4C}=\frac{3C{V}^2}{4}$

Work done in charging the capacitors $=$energy gained by the capacitors

$=\frac{3C{V}^2}{4}$