Question

A 100 μF capacitor is charged from a supply of 1000V, disconnected from the  supply and then connected across an uncharged 50 μF capacitor. 

Calculate the energy stored initially and finally in the  

two capacitors. What conclusion do you draw from a  

comparison of these results?

Answer 1

$$W_1=\frac{C_1V^2}{2}=\frac{100*10^{-6}*1000^2}{2}=50\:\rm J$$

$$q_1=C_1V=100*10^{-6}*1000=0.1\:\rm C$$

$$q_2=q_1$$

$$C_2=100\rm\: \mu F+50\: \mu F=150\:\mu F$$

$$W_2=\frac{q_2^2}{2C_2}=\frac{0.1^2}{2*150*10^{-6}}=33\:\rm J$$

The energy was lost.