Circuit Element
A circuit element is a basic unit that has certain rules governing the relationship of voltage across and current through that element beyond the simple conducting wire.
There are five ideal basic circuit elements:
- voltage source
- current source
- resistor
- capacitor
- inductor
There will be no proofs for the equations here. That's a physics thing that probably deserve their own page.
Ideal
This page will focus on ideal circuit elements. The real world is complicated; we make things convenient for ourselves by assuming certain properties despite being unrealistic. For example, an ideal voltage source outputs the same voltage regardless of current passing through it.
Resistor
The resistor dissipates energy depending on their resistance . They follow Ohm's Law:
The power disspated by a resistor can be calculated by
You can substitute and such that it only takes in one of them and the resistance.
Capacitor
The capacitor is one of two basic energy storing circuit elements (the other being the inductor). They gather charge depending on voltage and capacitance .
Taking time derivative on both sides, we have
The energy stored within a capacitor is given by
Inductor
The inductor is also an energy storing circuit element. They "resist" changes in current and stores energy based on inductance .
The energy stored within a capacitor is given by