Inductors and Capacitors – Important Concepts

Posted by Jeff Schuler on Sep 1, 2009 in Uncategorized |

I have already put a lot of material up related to inductors and capacitors, but more can’t hurt anyone.  I have a few new things to say about the inductor and the capacitor and a few different graphical approaches to common problems you will encounter in your electrical engineering classes.

/quick review

Inductors

Units of inductance are Henrys (H)

An inductor is made up of a coil, wrapped around a core, often magnetic.  A magnetic field is produced when a current flows through the wire.  With this changing current, an EMF is produced.  This EMF opposes any sudden changes in current.    This is a very important characteristic of an inductor.  An inductor tries to keep a circuit’s current constant by opposing any instant changes.

inductor-switching-circuit

An example! In the above schematic:  The switch in this circuit has been open for a very long time.  Immediately after the switch is closed, what is the current flowing through R1?

*Zero!  This is because the inductor opposes any immediate change in current, right after the closing of the switch, we would still have no current in the resistor.

Time constant ( τ) = L/R

V(t) = L \cdot \frac{dI}{dT} .  This equation means that a change in current must be present to produce a voltage across an inductor.

real-inductors

*Because the current cannot change suddenly, this results in a non-linear relationship of current vs. time.*

On LEFT:  Photos of a few common inductors.

inductor-response-curve

Energy stored:  The amount of energy stored in your inductor can be calculated as follows:

E = \frac{1}{2} L I^{2}

Adding Series Inductors

When you want to combine inductors to get your total inductance, simply add their values just as you would add resistors (when in series).

adding-series-inductors

If the inductors are in parallel, same procedure, manipulate them just as you would a resistor.

Capacitors

Units of Capacitance (Farads)

A capacitor is made up of two parallel plates, which store charge in your circuit.  The amount of charge the capacitor is able to store is directly proportional to the applied voltage.  This gives rise to the equation Q = C * V.  As you now know, inductors resist instant changes in current in a circuit.  A capacitor acts very similarly, only with voltage.  A capacitor’s voltage cannot change instantly, voltage in a capacitor must be built up, non-linearly.

charging-capacitorAbove right diagram:

Electrons are built up on the incoming current side of the capacitor, this process stores charge on the capacitor, which then distributes the voltage on to the resistor.  It takes five time constants to reach a maximum voltage, which explains the non-linear curve depicted to the left.

Time constant (τ) = RC * a capacitor reaches max voltage at approximately 5τ *

Energy stored:  The amount of energy stored in your capacitor can be calculated as follows:

E = \frac{1}{2} C V^{2}

Adding Series Capacitors

When you want to calculate total capacitance of a circuit, simply remember that the operation is opposite that of combining resistors.  When you have two capacitors in series, C1 and C2, the total capacitance is given by the following equation.

C_{eq} = (\frac{1}{C_{1}} + \frac{1}{C_{2}})^{-1}

Notice this is the same operation you use to combine two resistors in parallel.  With the same idea in mind, we can note how to combine two parallel capacitors.   With two capacitors in parallel: Ceq =  C1 + C2.  Just remember to treat inductors like resistors, and to treat capacitors just opposite, like conductors, when finding equivalent inductance, resistance, or capacitance.

/quick review

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2 Comments

DEAN
Sep 5, 2009 at 10:16 pm

One of the clearest explanations of basic inductive and capacitive theory that I have to date.


 
Jeff
Sep 6, 2009 at 12:56 am

Thank you dean, i’m glad you enjoyed the post. Tell your friends!


 

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