WEBVTT FILE 00:07.077 --> 00:13.100 Intersection of two networks is the set of branches and nodes that are in both networks. 00:13.100 --> 00:17.662 The intersection of these two networks are the nodes A, B, C, and E, 00:17.662 --> 00:24.659 and all branches, except those connecting the nodes A and D, D and C, and B and C. 00:24.659 --> 00:26.656 Two Kirchhoff networks are equivalent 00:26.656 --> 00:31.01 if each branch of their intersection has the same current in both networks, 00:31.01 --> 00:36.725 and each node pair of the intersection has the same voltage in the two networks. 00:36.725 --> 00:40.815 These two networks are equivalent. 00:40.815 --> 00:42.968 Next we will show procedures 00:42.968 --> 00:47.310 to obtain Kirchhoff networks equivalent to a given network. 00:47.310 --> 00:51.494 The first is to replace branches in series by a single branch. 00:51.494 --> 00:56.665 And the current common to the original branches is assigned to the new branch, 00:56.665 --> 01:01.558 and the sum of the voltages of the branches in series is assigned as its voltage. 01:01.558 --> 01:07.336 The branch replacing the branches in series is called resultant of the series branches. 01:07.336 --> 01:13.410 Thus, the resultant of the series branches has the same current as the branches it replaces, 01:13.410 --> 01:18.539 and its voltage is the sum of the currents of those branches. 01:18.539 --> 01:22.168 The reverse process also provides equivalent Kirchhoff networks: 01:22.168 --> 01:27.569 the branch connected between nodes A and C can be replaced by two or more branches in series, 01:27.569 --> 01:31.715 whose currents are equal to the current of the original branch, 01:31.715 --> 01:36.882 and whose voltages must add to the voltage of the original branch. 01:36.882 --> 01:42.010 Two or more parallel branches connected between two nodes can be replaced by a branch 01:42.010 --> 01:47.379 whose assigned current is the sum of the currents of the substituted branches, 01:47.379 --> 01:50.769 and whose voltage is the voltage of the extreme nodes. 01:50.769 --> 01:55.487 The branch replacing the parallel branches is called resultant. 01:55.487 --> 02:00.534 Therefore, the resultant of parallel branches has the same voltage they have 02:00.534 --> 02:06.014 and its current is the sum off the currents of the original branches. 02:06.014 --> 02:09.089 The inverse operation gives equivalent networks too: 02:09.089 --> 02:15.355 a branch can be replaced by parallel branches connected to the same terminals as the first branch, 02:15.355 --> 02:21.272 with currents such that their sum is the current of the original branch. 02:21.272 --> 02:26.169 If a part of a Kirchhoff Network is replaced with a node with any potential, 02:26.169 --> 02:30.532 then we get another Kirchhoff network equivalent to the first one. 02:30.532 --> 02:33.084 Indeed, the new network is a Kirchhoff network, 02:33.084 --> 02:36.633 because Kirchhoff's first law is met at the O node, 02:36.633 --> 02:38.808 as the currents leaving the node 02:38.808 --> 02:42.745 are the currents of the cut-set that connects parts A and B in the original network, 02:42.745 --> 02:45.574 thus their sum is zero. 02:45.574 --> 02:48.894 Kirchhoff's second law continues to be fulfilled in the new network, 02:48.894 --> 02:52.853 because its voltages derive from node potentials. 02:52.853 --> 02:57.966 All branches of the new network have the same current as in the first network, 02:57.966 --> 03:03.028 and all nodes in the intersection have the same potentials in both networks, 03:03.028 --> 03:06.906 so that the two networks are equivalent. 03:06.906 --> 03:11.165 The inverse operation also creates a network equivalent to the first network. 03:11.165 --> 03:14.977 It consist in replacing a node by some part of a Kirchhoff network 03:14.977 --> 03:19.294 which connects to the initial part with the branches converging at the eliminated node, 03:19.294 --> 03:22.412 which are a cut-set. 03:22.412 --> 03:26.191 That is, a Kirchhoff network equivalent to other can be obtained 03:26.191 --> 03:28.530 by performing any modification that leaves unaltered 03:28.530 --> 03:33.756 the currents and voltages of the intersection of both networks. 03:37.702 --> 03:41.200 Subtitles and English translation: Roberto C. Redondo Melchor.