Time Constants??? Really???

Yes I am afraid so.

Learning the concept of time constants in a DC circuit provides us with a good foundation for understanding how an inductor behaves in an AC circuit.

Ok, but I have heard that they are really hard.

Truth be told (or TBT as the cool kids text) they can be.  That being said they don’t have to hard at all.  In fact there is a method that makes them quite easy.

Teach me.

There are three methods for determining the currents at different time constants.  All of them are based off of the steady state current (V source/resistance)

1- Remembering that each time constant takes 63.2% of the the former current.

This can be a cumbersome way to calculate current.  For example lets use 10 amps as the steady state current:

1st T.C:

10 x 63.2% =6.32 Amps (Easy right?)

2nd T.C. :

10 – 6.32 = 3.68

3.68 x 63.2%=2.32

6.32 + 2.32 = 8.64 Amps

3rd T.C. :

10- 8.64 = 1.36

1.36 x 63.2% = .859

8.64 + .859 = 9.5 Amps

4th T.C :

10- 9.5 = .5

.5 x 63.2% = .316

9.5 + .316 = 9.8 Amps

5th T.C. :

10-9.8 = .2

.2 x 63.2% = .126

9.8 + .126 = 9.93 Amps

At the 5th time constant we can say that for all intents and  purposes that it is at steady state current.

This method will work for you but it is cumbersome and there is a lot of room for errors.

2- Use the percentages

If you look at the above example you can see that:

1st  T.C = Steady state current x 63.2%

2nd T.C. = Steady state current x 86.4%

3rd T.C. = Steady state current x 95%

4th T.C. = Steady state current x 98.1%

5th T.C. = Steady state current x 99.3% (or 100%)

It will work every time.  The only issue is you have to have a memory for numbers.

3- The sexy way

This method involves using your calculator and something called Napiers constant.

This method will make women swoon and men fall to their knees.  Yes it is sexy AF.

How do you do it?  Watch the video to find out.

It takes some practice but trust me when I say it will become your preferred method.

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