Circuits

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

By G. Williams (auth.)

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27(a) shows a network consisting of resistances and sources connected via two terminals A and B to a load branch RL. The network is said to be a two-terminal or one-port network. 27(b) and it consists of VT, the Thevenin equivalent source, and RT, the Thevenin equivalent resistance. The value of VT is the voltage which would exist across terminals A and B if RL were removed. This may be explained by reference to fig. 28. If a variable voltage source is inserted between the network and the load as shown then the value of Vn may be adjusted until the current flowing in the load is zero (that is, iL = 0).

There is thus a very large number of ways in which the variables may be chosen. Assuming that the branch voltages and currents are chosen as the 2b variables, a set of independent equations 2b in number must now be determined. Consider first the branch volt-ampere equations. If the branch is, say, a resistance then the voltampere equation is v =Ri and as there are b branches there must obviously be b independent volt-ampere equations. The branch volt-ampere equations thus provide half the required number of equations (that is b).

Consider the circuit shown in fig. 8(a). Suppose it is necessary to construct its dual. By observation the network has three meshes (A, B, and C); ten branches (1-I 0) and 7 independent nodes (a, b, c, d, e, f and h with reference to the ground node g). The dual network must therefore consists of three independent nodes (A, Band C with reference to a ground node G); ten branches (1-IO) and seven meshes (a, b, c, d, e, f and h with an outer space g). Setting out three nodes A, Band C and a ground node Gas shown in fig.

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