Download e-book for iPad: An Introduction to Electrical Circuit Theory by G. Williams (auth.)

By G. Williams (auth.)

ISBN-10: 0333233859

ISBN-13: 9780333233856

ISBN-10: 1349036374

ISBN-13: 9781349036370

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Extra info for An Introduction to Electrical Circuit Theory

Sample text

The equations obtained from the application of Kirchhoffs current law to each node obviously yields n current equations but are they independent? 1. The first branch between the ground node and the node a provides only one current equation because only one current exists and it flows through both nodes. But the addition of any other node provides an additional current equation and each additional current equation must be independent because it includes a parameter not included before, namely the branch necessary to set up a new node.

The voltage-law equations for the topological meshes are mesh acb R 2 i1 + R 5 (i1 mesh bed R4i 2 + R 3(i 2 i 2 ) + R1 (i1 - - i 3) = 0 - i 3 ) + R s(i 2 - i1) =0 The constraint equation is i3 =I and thus two equations remain to solve for two unknowns. Constrained node voltages A similar technique to the constrained mesh current method is available for the treatment of resistanceless voltage sources. In the discussion on source substitutions it was shown that a resistanceless voltage source introduced an apparent or pseudo node into a network.

5 repeated. It is required to find the equivalent resistance of the circuit between points A and B. The star network between nodes a, c and b with its centre at node b may be replaced by an equivalent delta. 19) gives Rae R~ = (2 X 3) + (3 = (2 X 3) + (3 X 4) + (4 X 2) = 26 = 6 S Q . 4 X 4) + (4 X 2) = 26 13 Q 4 2 2 and R ct= (2 x 3) + (3 x 4) + (4 x 2) = 26 = 8 i a 3 3 n The equivalent circuit is then as shown in fig. 26(b ). The parallel resistances between nodes a and c and nodes c and d may then be combined into single resistances as shown in fig.

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An Introduction to Electrical Circuit Theory by G. Williams (auth.)


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