WEBVTT FILE 00:07.823 --> 00:10.176 A port of a Kirchhoff multi-terminal network 00:10.176 --> 00:12.054 is constituted by a set of terminals 00:12.054 --> 00:16.300 whose summation of currents is constant and zero. 00:16.300 --> 00:18.626 Every Kirchhoff multi-terminal network has at least 00:18.626 --> 00:21.641 one port consisting of all its terminals, 00:21.641 --> 00:24.699 because the sum of the currents of all the terminals is zero. 00:25.199 --> 00:30.523 If this is a Kirchhoff network, the branches connecting B and A are a cut set, 00:30.523 --> 00:33.701 thus the currents of these branches add up to zero. 00:33.701 --> 00:39.096 So, all these branches constitute a port of the multi-terminal network A. 00:39.096 --> 00:43.753 Similarly, all branches connecting C and A are a port of A. 00:43.753 --> 00:47.098 And so are the branches connecting D and A. 00:47.098 --> 00:53.802 A is a multi-terminal network with several ports, thus it is called multiport network. 00:53.802 --> 00:58.371 Note that the union of two ports is another port. 00:58.871 --> 01:02.637 The Kirchhoff power absorbed by a multi-terminal network through a port 01:02.637 --> 01:06.905 is the sum of the products of the potential of each terminal of the port 01:06.905 --> 01:10.188 by its corresponding current. 01:10.188 --> 01:15.966 Its opposite is the Kirchhoff power delivered by the multi-terminal network through that port. 01:15.966 --> 01:19.983 It turns out that the Kirchhoff power absorbed by a multi-terminal network through a port 01:19.983 --> 01:23.150 does not depend on the where the potential reference is. 01:23.150 --> 01:25.814 Indeed, for a given potential reference, O, 01:25.814 --> 01:30.157 the Kirchhoff power absorbed by the port is 'p-sub-g1'. 01:30.157 --> 01:32.853 If another potential reference is chosen, O', 01:32.853 --> 01:36.719 the new potential of the k terminal, is the former potential 01:36.719 --> 01:40.399 plus the potential difference between O and O'. 01:40.399 --> 01:46.020 And now the Kirchhoff power absorbed by the port is 'p-sub-g2'. 01:46.020 --> 01:51.106 But, since the sum of the currents of the branches of a port is zero, 01:51.106 --> 01:54.835 this power is the same as the power absorbed by the port 01:54.835 --> 01:58.035 with the original potential reference. 01:58.035 --> 02:01.833 Therefore, the Kirchhoff power absorbed by a multi-terminal network through a port 02:01.833 --> 02:06.117 can be measured by as many meters as terminals in the port. 02:06.117 --> 02:12.146 Or with one meter less, if a terminal of the port is chosen as potential reference. 02:12.646 --> 02:17.604 Two ports are disjoint if they have no terminal in common. 02:17.604 --> 02:22.262 If the union of disjoint ports is the set of all terminals of the multi-terminal network, 02:22.262 --> 02:24.720 the Kirchhoff power absorbed by the multi-terminal network 02:24.720 --> 02:29.724 is the sum of the power absorbed by those disjoint ports. 02:30.274 --> 02:33.999 The ports of a multiport network are frequently classified into 02:33.999 --> 02:37.852 input ports and output ports. 02:37.852 --> 02:41.705 The Kirchhoff power absorbed by the multi-terminal network through the input ports 02:41.705 --> 02:45.724 is the input power of the multi-terminal network. 02:45.724 --> 02:48.879 And the power delivered by the multi-terminal network through the output ports 02:48.879 --> 02:52.831 is the output power of the multi-terminal network. 02:52.831 --> 02:56.271 The power absorbed by the multi-terminal network is the difference between 02:56.271 --> 03:01.931 the sum of the input powers and the sum of the output powers. 03:02.431 --> 03:06.800 Transformers and electric lines are just two examples of multiport network. 03:06.800 --> 03:09.307 But there are many more. 03:13.588 --> 03:17.228 Subtitles: Roberto C. Redondo Melchor.