I have basically two questions in mind,which are
- Why expression of energy occurs in triplet?
- Why the expressions are somewhat symmetrical?
Coming to elaborated form of 1st part, we have
The above expressions are for the energy stored in capacitors.
These are for heat dissipation in resistor.
See in both cases the energy occurs in triplet. There are several other examples, too, in thermodynamics. I want to ask here: Why nature favours $3$ in physics?
Now the second part of the question says why the expressions are quite symmetrical?
Are both parts of the question a coincidence, or something else?