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The Inductor – Part II

The Inductor circuit.

The Inductor circuit.

In the last electrical post “Through the Looking Glass – Duality – The Inductor“, I spent a lot of time building up the fundamentals of electromagnetism and what is going on inside the inductor.  I also probably over-used the “twisted sister” analogy, but I will continue with that because we are just now getting into the twisted differences.

The DC plot for an inductor.

The DC plot of current for an inductor-resistor circuit.

When the switch is closed to connect the inductor and resistor to the battery, the inductor develops a CEMF to oppose the battery voltage.  It takes time for the current to increase in the circuit and for the field to build.   With the capacitor it was voltage that took time to build.  This is the duality… the same, but different.

The formula for the time constant in an inductor and resistor circuit, LR circuit, is:  tc = L/R.   This means that the bigger the inductor the longer the time constant and the bigger the Resistor the shorter the  time constant.   Again, a twisted image of the capacitor circuit.   The tc for our circuit is:  1 mH / 1KΩ or 1 μsecond.

The voltage across the inductor when closing the switch.

The voltage across the inductor in the LR circuit when closing the switch.

The Voltage across the inductor when the switch is closed looks like the plot to the right.   The inductor looks like an open circuit at the first moment the switch is closed and eventually after many time constants later it looks like a wire.  Again just the exact opposite of a capacitor.

Another way to think of an inductor is as electrical inertia,   Just like trying to push a heavy weight on rollers (for example a train), the current has a hard time starting to flow and it takes it some time to get moving. The formulas for the circuit we have just talked about are:

I and Vl DC closing switch

The twists about to get stranger.  What happens when the switch is opened? 

The inductor wants to maintain current constant.   When we first applied voltage and the inductor was with zero current and wanted to remain that way.   However, once current is flowing the inductor also wants to remain with current flowing and in the same direction.   Remember the fields are built and an attempt to stop current will cause those fields to collapse and a moving field induces a voltage.  The energy of the built field is stored in the inductor and must be released.   For our first example, imagine the inductor circuit has been operating with the battery for a long time (greater than 5 time constants).  Next imagine the two position switch in the diagram is immediately switched from the battery to the wire.  The current flowing in the circuit at that instant would remain the same as before and then drop with the same exponential time constant as it did building.

How can it do this, there is no battery in the circuit?   At the time the switch is flipped the voltage across the inductor immediately changes polarity and it drives the current in the same direction as before.

What would happen if the switch was opened and there was no place for the current to go?   The field must collapse.  The energy stored within the inductor must be dissipated.  If the switch is opened and no way to dissipate the energy the inductor will find a way.  The voltage on the inductor will increase until it finds a current path.   Normally this is across the opening contacts of the switch and it will produce a spark.  If the inductor is large the stored energy is large and the spark will be large.  I actually have a “war story” about this in a project but there are a few more things we need to talk about before you can follow the complete story.

This “must dissipate” the stored energy is a very big difference between a capacitor and an inductor.   An inductor has no way of maintaining the energy while a capacitor is very happy to maintain the voltage for a long time.   (I have a “war story” about that too.)    As long as we understand the differences and the properties we can not only tolerate them, but there are many uses for the collapsing field.

The unit of a the size of an inductor is the Henry.   The symbol is H and one Henry is defined as 1 volt CEMF produced for a change in current of 1 A per second.   Inductors can range in size from μH values to many Henry’s.   Every conductor has some value of inductance because a field is developed around every conductor.   Most often this is not important.

A few more differences:

When we put capacitors in series we decreased the the capacitance.  When we put inductors in series the total inductance is equal to the sum assuming that there is no interaction in the fields of the two inductors.

When we put capacitors in parallel to each other the total capacitance is equal to the sum.   When we put inductors in parallel to each other the total inductance is equal to the formula Lt = 1/(1/L1 + 1/L2 + 1/L3….) again assuming no interaction of the fields.  The rules for an inductor are exactly the same as those for resistors and the rules for capacitors are the exact opposite.

This pretty much completes everything for inductors in DC.   Soon I will start talking about them in AC.   However, it is time first to get back into reality and back to the make part of create and make.

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