FHSST Physics/Electronics/Capacitive and Inductive Circuits

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A capacitor[edit]

A capacitor is simply two conductors separated by a dielectric (insulator). A capacitor (historically known as a "condenser") is a device that stores energy in an electric field .

The most common kind of capacitor has two parallel plates with a (fairly) uniform electric field between the plates.

A battery can be used to fill one end of the capacitor with electrons and drain electrons from the other end of the capacitor. This is known as charging. Charging a capacitor creates a charge imbalance between the two plates and creates a voltage that stops the capacitor from charging. When capacitors are connected to a battery, current flows only until the capacitor becomes charged to the same voltage as the battery. When the capacitor is charged to the same voltage as the battery, current stops flowing -- the capacitor acts like an open circuit. It is as if the capacitor gained infinite resistance.

If we pull a capacitor out of the circuit, it retains the voltage to which it was charged. (In real capacitors, the excess electrons on one plate slowly leak over to the other plate. But the higher the quality of the capacitor, the closer it acts like an "ideal capacitor". An "ideal capacitor" would hold that charge forever. )

Just as the capacitor charges it can be discharged.

An inductor[edit]

If we are going to talk of inductive circuits we need a definition of a inductor.

An inductor is simply a coil of wire (or some other conductive material). An inductor is a device which stores energy in a magnetic field.

An inductor only resists changes in current. An ideal inductor does not offer any resistance to direct current, except when the current is switched on and off, in which case it makes the change more gradual. However, all real-world inductors are constructed from material with finite electrical resistance, which opposes even direct current.

Whenever current flows, it creates a magnetic field proportional to the current. (In other words, whenever electrons move, they create a magnetic field -- proportional to both how many electrons there are, and how fast their average speed is). Coiling the wire concentrates that field inside the coil.

A changing magnetic field always induces a voltage in any wire.

When we apply a voltage source to the inductor -- for example, when we energize the field winding of an electric fan by plugging it in -- the current will flow through the coil, creating a magnetic field.

As more and more current flows, the magnetic field also increases proportionally. The changing magnetic field creates a "back-emf" (the voltage across the coil). That same wire, when straightened out, would act like a short circuit -- but when formed into a coil, much less current goes through it.

If we applied a constant DC voltage to this coil, the current would keep increasing more and more, until something failed.

As you know, the voltage supplied by the wall socket isn't DC. It returns to zero then increases in the opposite direction many times a second.

When the voltage returns to zero, the current through the inductor stays constant -- the constant current causes a constant magnetic field, the constant magnetic field causes zero "back-emf". When the supply voltage reverses direction, the current through the coil decreases, causing the magnetic field to decrease. Because the magnetic field is decreasing, it induces a "back-emf" voltage across the inductor in the opposite direction than when the magnetic field was increasing. (Something interesting happens after the magnetic field decreases all the way to zero, but we don't have time to talk about that).

To summarize, at first, the current through the coil goes from + to -, just like a resistor or a charging capacitor. But just after the voltage reverses, the current continues going in the same direction, which is now - to +. This makes inductors unlike any other component known to mankind. We say that "in an inductor, the voltage leads the current" or ELI.


Normally inductors are made of copper wire, but not always (Example: aluminum wire, or spiral pattern etched on circuit board). The material around and within the coil affects its properties common types are air-core (only a coil of wire), iron-core, and ferrite core. Iron and ferrite types are more efficient because they conduct the magnetic field much better than air. Ferrite is more efficient than iron because stray electricity cannot flow through it.

Fhsst magnify.png Some inductors have more than a core, which is just a rod the coil is formed about. Some are formed like transformers, using two E-shaped

pieces facing each other, the wires wound about the central leg of the E's. The E's are made of laminated iron/steel or ferrite.

Some inductors have more than a core, which is just a rod the coil is formed about. Some are formed like transformers, using two E-shaped pieces facing each other, the wires wound about the central leg of the E's. The E's are made of laminated iron/steel or ferrite.

Important qualities of an inductor:

There are several important properties for an inductor.

  • Current carrying capacity is determined by wire thickness.
  • Q, or quality, is determined by the uniformity of the windings, as well as the core material and how thoroughly it surrounds the coil.
  • Last but not least, the inductance of the coil.

The inductance is determined by several factors.

  • coil shape: short and squat is best
  • core material
  • windings: winding in opposite directions will cancel out the inductance effect, and you will have only a resistor.

A comparison of capacitors and inductors[edit]

  • In capacitors, current leads voltage.
  • In inductors, voltage leads current.

I remember this by saying "ELI the ICE man".

See: