By G. Williams (auth.)
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Extra resources for An Introduction to Electrical Circuit Theory
26( d) is combined into a single resistance as shown in fig. 26(e). 11. 11. 11. 11. 26 (e) Circuit simplification by successive star-delta transformations 2. 6 leads to a more general method for dealing with complicated linear networks. The method described here will reduce any finear network connected between two terminals to a single voltage source in series with a single passive branch. Networks containing linear capacitances and inductances may also be treated by this method and similar results may be obtained.
5 by mesh analysis. Assign three clockwise mesh currents as iOI. ) + 2(i01. - i13 ) + 4(i01. ) = 0 mesh abd mesh acb mesh bed Simplifying gives = 10 -2i01. 3- 3i'Y = 0 -4i01. 3- 4i'Y Thus three equations exist to determine the three unknown mesh currents. 3; the matrix of the coefficients of the equations is rl-4~~ :~ =; -3 +9 about which the following points should be noted: (i) All the terms on the principal diagonal are positive (ii) All the other terms are negative (iii) The matrix is symmetrical about the principal diagonal All the terms may be written down by inspection from the problem.
11. 11. 11. 26 (e) Circuit simplification by successive star-delta transformations 2. 6 leads to a more general method for dealing with complicated linear networks. The method described here will reduce any finear network connected between two terminals to a single voltage source in series with a single passive branch. Networks containing linear capacitances and inductances may also be treated by this method and similar results may be obtained. The method is described by Thevenin's theorem which states: 'A linear network containing sources which is connected between two terminals may be replaced by an equivalent voltage source in series with an equivalent passive branch.