Adding stripped down 6002x course for testing, along with CMS test for edit pages for same

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Calen Pennington
2012-07-17 10:42:47 -04:00
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Clarification of the term "Linear"
<p>
The term "linear" is very clear when applied to a
mathematical function. A function F is linear if and only
if it obeys homogeneity and superposition:
</p><p>
Homogeneity: F(cx) = cF(x)
<br/>
Superposition: F(x+y) = F(x) + F(y)
</p><p>
In the context of what we have seen so far, the only
elements that are linear as mathematical functions are
resistors. An independent voltage source or an independent
current source is not a linear element. (There are also
linear dependent sources, linear
inductors, and other linear elements, but we have not yet introduced them in our class.
You will see them later.)
</p><p>
Formally, a circuit composed of only linear elements is a
linear circuit. When we add independent sources to a linear
circuit as inputs, we get a circuit that is not linear
because it has an offset: its v-i characteristic at a pair
of exposed terminals may not pass through the origin.
However, we can make a Thevenin or Norton equivalent model
of such a circuit: the Thevenin resistance summarizes the
effect of the linear elements and the Thevenin voltage
summarizes the effect of the independent sources.
</p><p>
However the term "linear," when applied to an electrical
circuit often takes on an informal meaning. We often say
that a circuit containing only linear elements and
independent sources is a "linear circuit." So, in the
informal sense, a linear circuit is one where we can apply
the Thevenin or Norton theorems to summarize the behavior at
a pair of exposed terminals.
</p><p>
Sorry for the confusion of words -- natural language is like
that!
</p>