WEBVTT FILE 00:10.404 --> 00:18.393 This lesson shows an easy way to assign values that meet Kirchhoff's first law to the branches of a network. 00:18.393 --> 00:26.725 The expression ‘oriented branch’ distinguishes between the AB branch, and its opposite branch, the BA branch. 00:26.725 --> 00:33.174 The expression ‘non-oriented branch’ considers AB and BA as just one branch. 00:33.174 --> 00:42.609 Therefore, if ‘r’ is the number of non-oriented branches in a network, the number of oriented branches is ‘2r’. 00:42.609 --> 00:53.986 Similarly, the expression ‘oriented path or loop’ distinguishes between the ABCDA path, and its opposite path ADCBA. 00:53.986 --> 01:00.395 Conversely, ‘non-oriented path’ considers both oriented paths as one. 01:00.395 --> 01:05.078 The numbers and functions assigned to the branches of the network are Kirchhoff currents, 01:05.078 --> 01:08.581 because they meet Kirchhoff's first law. 01:08.581 --> 01:15.334 A network with Kirchhoff currents assigned to its branches is called ‘network of Kirchhoff currents’. 01:15.334 --> 01:19.909 Therefore, this network is a network of Kirchhoff currents. 01:19.909 --> 01:23.883 The process of assigning Kirchhoff currents to networks can be difficult, 01:23.883 --> 01:28.540 because it is necessary to find values that meet Kirchhoff's first law. 01:28.540 --> 01:32.977 But there is a procedure that simplifies this process considerably. 01:32.977 --> 01:39.653 It consists of assigning any value to each oriented loop, and the opposite value to the opposite loop. 01:39.653 --> 01:45.692 For example, the ABCDA loop is assigned ‘-j’. 01:45.692 --> 01:53.404 Which means that the opposite loop ADCBA is assigned ‘j’. 01:53.404 --> 01:56.251 And so on for the rest of the loops. 01:56.251 --> 02:03.528 It is understood that the loop BCEB, for which there is no specified value, is assigned the value ‘zero’. 02:03.528 --> 02:06.804 Similarly for AEBA. 02:06.804 --> 02:11.851 The values thus assigned to the loops are called ‘loop currents’. 02:11.851 --> 02:18.210 If each branch is assigned the sum of the currents of the loops that the branch belongs to, 02:18.210 --> 02:21.982 then those values are said to derive from loop currents. 02:21.982 --> 02:26.442 For example, the AB branch is assigned ‘-j’. 02:26.442 --> 02:30.202 The DA branch is assigned ‘e to the x, minus j’. 02:30.202 --> 02:32.788 And so on for all the network. 02:32.788 --> 02:36.606 If the values assigned to the branches derive from loop currents, 02:36.606 --> 02:42.863 they fullfil Kirchhoff's first law; that is, they are Kirchhoff currents. 02:42.863 --> 02:46.010 To prove this property let us consider the node D, 02:46.010 --> 02:51.377 and the fact that the currents of all the branches arriving to it derive from loop currents. 02:51.377 --> 02:55.142 Then, in the current of any branch, such as the CD branch, 02:55.142 --> 03:03.988 ‘i sub 1’ appears as addend, and in the current of AD appears ‘minus i sub 1’. 03:03.988 --> 03:09.450 So that in the sum of the currents arriving to D, ‘i sub 1’ vanishes. 03:09.450 --> 03:15.515 And the same happens to the other loop currents passing through the node D. 03:15.515 --> 03:18.998 And, in the same way, for the rest of the nodes. 03:18.998 --> 03:21.170 Specifically, for the A node: 03:21.170 --> 03:31.724 ‘i sub DA, plus i sub EA, plus i sub BA’ is equal to ‘i sub 1 plus i sub 2, minus i sub 1, minus i sub 2’, 03:31.724 --> 03:34.292 which equals zero. 03:34.292 --> 03:36.727 And the same is true for the rest of the nodes. 03:36.727 --> 03:45.576 Therefore, assigning arbitrary currents to the loops is a sure way to get Kirchhoff currents for any network. 03:48.870 --> 03:51.467 Subtitles and English translation: Roberto C. Redondo Melchor.