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278 ⏐⏐⏐ METHODS OF ANALYSIS AND SELECTED TOPICS (dc)
FIG. 8.39
Using Mathcad to verify the numerical calculations of Example 8.18.
Solution 2: Using the TI-86 calculator:
det[[11,�3,15][�3,10,0][�8,�5,0]]/det[[11,�3,�8][�3,10,�5][�8,�5,23]] ENTER 1.220
CALC. 8.3
This display certainly requires some care in entering the correct
sequence of brackets in the required format, but it is still a rather neat,
compact format.
8.9 NODAL ANALYSIS (GENERAL APPROACH)
Recall from the development of loop analysis that the general network
equations were obtained by applying Kirchhoff’s voltage law around
each closed loop. We will now employ Kirchhoff’s current law to
develop a method referred to as nodal analysis.
A node is defined as a junction of two or more branches. If we now
define one node of any network as a reference (that is, a point of zero
potential or ground), the remaining nodes of the network will all have a
fixed potential relative to this reference. For a network of N nodes,
therefore, there will exist (N �1) nodes with a fixed potential relative to
the assigned reference node. Equations relating these nodal voltages can
be written by applying Kirchhoff’s current law at each of the (N �1)
nodes. To obtain the complete solution of a network, these nodal voltages
are then evaluated in the same manner in which loop currents were
found in loop analysis.
N A