Sharing charge and energy

You will write three functions that describe two capacitors that are joined together.

The idea. When two charged capacitors are joined, the charge is shared and the voltages become equal. The energy is not conserved. Some of it is lost. A charge of one sign can cancel a charge of the other sign, so write the voltage of a capacitor joined the wrong way round as a negative number.

Your tasks.

1. In stored_energy, return $\tfrac{1}{2}CV^2$ for $C$ in $\mu\text{F}$ and $V$ in V. The answer is in $\mu\text{J}$.
2. In common_voltage, return the voltage after the two capacitors are joined, in V.
3. In energy_lost, return the energy before joining minus the energy after joining, in $\mu\text{J}$.