File:Two capacitor paradox.svg

English: Circuit illustrating the two capacitor paradox, a well-known paradox in electric circuit theory. It shows two identical capacitors ${\displaystyle C}$ in parallel connected by an open switch. Initially one of the capacitors is charged to an initial voltage ${\displaystyle V_{i}}$, the other is uncharged. When the switch is closed, charge flows from the charged capacitor on the left into the uncharged capacitor on the right, lowering the voltage on the left capacitor and raising the voltage on the right capacitor. When the current stops flowing, the two capacitors will have equal charges and equal voltages of ${\displaystyle V_{i}/2}$. The initial energy ${\displaystyle W_{i}}$ in the circuit is the energy stored in the left capacitor:

${\displaystyle W_{i}={1 \over 2}C{V_{i}}^{2}}$

The final energy in the circuit is the sum of the energy in the left and right capacitor:

${\displaystyle W_{f}={1 \over 2}C({V_{i} \over 2})^{2}+{1 \over 2}C({V_{i} \over 2})^{2}}$

${\displaystyle W_{f}={1 \over 4}C{V_{i}}^{2}}$

The final energy is half the initial energy. Where did the other half of the initial energy go?