WEBVTT FILE 00:08.123 --> 00:11.035 Let us consider any surface S. 00:11.035 --> 00:13.747 If electrical charge passes through that surface 00:13.747 --> 00:18.212 we say that there is electrical current through that surface. 00:19.257 --> 00:20.884 Let us denote by q-sub-AB 00:20.884 --> 00:24.606 the time-dependent function which gives the charge that has crossed from A to B 00:24.606 --> 00:27.772 in each value of time t. 00:27.772 --> 00:29.653 And by "increment of q-sub-AB" 00:29.653 --> 00:32.521 to the charge that has crossed from A to B 00:32.521 --> 00:35.434 minus the one that has crossed from B to A 00:35.434 --> 00:40.536 in the same time interval of duration "increment of t". 00:40.536 --> 00:44.108 Thus, if for 3 seconds the charges that cross from A to B 00:44.108 --> 00:47.166 are 5 Coulombs and -7 Coulombs, 00:47.166 --> 00:49.203 and from B to A cross 00:49.203 --> 00:52.371 8 Coulombs and -4 Coulombs, 00:52.371 --> 00:55.938 the charge that crossed during that time from A to B is 00:55.938 --> 00:59.804 -6 Coulombs. 01:00.800 --> 01:02.514 And the "increment of q-sub-BA" 01:02.514 --> 01:06.193 is the charge that crosses at the same time from B to A 01:06.193 --> 01:08.944 minus the charge that crosses from A to B, 01:08.944 --> 01:12.398 6 Coulombs. 01:12.398 --> 01:15.332 The charge that crosses from B to A is always 01:15.332 --> 01:20.638 the opposite of the one that crosses from A to B. 01:20.638 --> 01:23.332 Therefore, saying that from A to B 01:23.332 --> 01:26.391 has crossed the charge "increment of q-sub-AB" 01:26.391 --> 01:29.516 means the same as saying that from B to A 01:29.516 --> 01:34.126 has crossed the charge "-increment of q-sub-AB". 01:35.501 --> 01:39.657 The quotient between the charge that crosses the S surface from A to B, 01:39.657 --> 01:41.507 and the time it takes to cross it, 01:41.507 --> 01:44.244 is called the average current 01:44.244 --> 01:48.421 in that time interval from A to B. 01:48.421 --> 01:51.923 Therefore, the average current i-sub-AB is: 01:51.923 --> 01:55.610 charge that, on average, crosses the surface S 01:55.610 --> 02:00.177 each time unit from A to B. 02:00.177 --> 02:03.269 Its unit in the International System turns out to be 02:03.269 --> 02:06.900 Coulomb per second, which is called Ampere, 02:06.900 --> 02:11.145 and its symbol is a capital A. 02:11.145 --> 02:15.664 As the elapsed time t is always positive, 02:15.664 --> 02:20.874 i-sub-AB always has the same sign as q-sub-AB. 02:20.874 --> 02:23.453 Also, since "increment of q-sub-BA" 02:23.453 --> 02:26.359 is the oposite of q-sub-AB 02:26.359 --> 02:29.658 it turns out that the current from B to A 02:29.658 --> 02:35.529 is opposite to the current from A to B. 02:35.529 --> 02:38.115 Thus, if in a range of 3 second 02:38.115 --> 02:41.950 the charge crossing from A to B is -6 Coulombs, 02:41.950 --> 02:44.422 the average current from A to B 02:44.422 --> 02:47.226 is -2 amperes, 02:47.226 --> 02:51.660 and from B to A it is 2 amperes. 02:51.660 --> 02:54.716 Therefore, saying that i-sub-AB 02:54.716 --> 02:57.051 is the current from A to B 02:57.051 --> 02:59.578 means exactly the same as saying that 02:59.578 --> 03:05.435 the current from B to A is "-i-sub-AB". 03:06.703 --> 03:10.572 As we reduce the time in which the average current is calculated, 03:10.572 --> 03:14.560 that average current approaches the current in an instant. 03:14.560 --> 03:18.461 This is why we call instantaneous current from A to B 03:18.461 --> 03:23.094 to the average current, when the time range approaches zero. 03:23.094 --> 03:29.09 That is to say, to the derivative of the charge q-sub-AB with respect to the time. 03:29.09 --> 03:32.940 As the charge q-sub-BA is the opposite of q-sub-AB, 03:32.940 --> 03:35.397 the instantaneous current from B to A 03:35.397 --> 03:40.000 is the opposite of the instantaneous current from A to B. 03:43.030 --> 03:45.200 For example, if the charge q-sub-AB 03:45.200 --> 03:47.597 is given in each time by the function 03:47.597 --> 03:50.199 Sine of (Pi t) minus 2, 03:50.199 --> 03:53.620 the instantaneous current in a given time t is 03:53.620 --> 03:57.361 Pi times the Cosine of (Pi t). 03:57.361 --> 04:00.995 Tha function gives the instantaneous current from A to B 04:00.995 --> 04:03.763 for any given value of t. 04:07.329 --> 04:10.453 Subtitules and English translation: Roberto C. Redondo Melchor