Simple Electrical Circuits are often represented by Resistors, Capacitors, Inductors and Voltage Sources.
- Resistors have a Resistance to DC, and an Impedance to AC which equals the Resistance at all frequencies.
- Capacitors have infinite resistance to DC, and an Impedance to AC which reduces with increasing frequency.
- Inductors have zero resistance to DC, and an Impedance to AC which increases with increasing frequency.
- Voltage sources may be DC (simpler) or AC (more complex):
- Direct Current voltage sources means that the voltage has a constant value, and current always flows in the same direction. DC circuits mostly have resistors and DC voltage sources. The current and voltage at each point in the circuit can be represented as "real" numbers. In a DC circuit, an inductor looks like a zero resistor, and a capacitor can be considered an infinite resistor (if you wait long enough).
- Alternating Current means that the voltage is continually changing, usually in a "sine wave", which is shaped like ripples on a pond. The "amplitude" represents the amount that the top & bottom of the ripple differs from the "average" value. AC also has a "phase", which represents where the AC cycle is in its range from top to bottom (and back again) and a "frequency", which represents how quickly it cycles through these conditions. The current and voltage at each point in the circuit must be represented as "complex" or "imaginary" numbers ("imaginary" is an unfortunate and obsolete term that was coined before lots of really practical applications were found for them). AC currents can flow through capacitors, inductors and resistors to different extents depending on the frequency, and experience different phase shifts depending on frequency.
- There is an intermediate form of "transient analysis", where you apply a DC signal to a circuit, and the voltage on capacitors and inductors jumps around for a while until it settles down to a normal DC circuit. This has some characteristics of DC and AC circuits
In one sense, a DC voltage source can be considered to be an AC source with zero frequency, which means it will easily flow through inductors, and somewhat easily through resistors, but not through capacitors.
Often, a voltage will represent a complex shape like a voice, which can be considered as DC plus sine waves of many different frequencies added together (
Fourier analysis).
Practical circuits contain components like transistors, whose properties change over time, dependent on input voltage or current; this can produce even more complex behaviours like sustained oscillations or chaotic behaviour (or a Turning machine).