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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} . They follow Ohm's Law:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v = ir }

The power disspated by a resistor can be calculated by

$p=iv$

You can substitute Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v} 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C} .

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q = CV }

Taking time derivative on both sides, we have

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i = C \frac{dv}{dt} }

The energy stored within a capacitor is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W = \frac{1}{2} C V^2 }

Inductor

The inductor is also an energy storing circuit element. They "resist" changes in current and stores energy based on inductance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L} .

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V = L \frac{di}{dt} }

The energy stored within a capacitor is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W = \frac{1}{2} L I^2 }