[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:03.48,Default,,0000,0000,0000,,>> Now, let's consider how we combine
Dialogue: 0,0:00:03.48,0:00:07.94,Default,,0000,0000,0000,,impedances that are connected in\Neither series or in parallel.
Dialogue: 0,0:00:07.94,0:00:10.29,Default,,0000,0000,0000,,We might get a hint from\Nthe fact that because
Dialogue: 0,0:00:10.29,0:00:12.42,Default,,0000,0000,0000,,impedances have the units of ohms,
Dialogue: 0,0:00:12.42,0:00:14.64,Default,,0000,0000,0000,,we would expect them to combine in
Dialogue: 0,0:00:14.64,0:00:16.68,Default,,0000,0000,0000,,exactly the same way that resistances
Dialogue: 0,0:00:16.68,0:00:19.18,Default,,0000,0000,0000,,do and we're going to see\Nthat is in fact the case.
Dialogue: 0,0:00:19.18,0:00:24.39,Default,,0000,0000,0000,,So for example, we've got Z_1 and Z_2\Nconnected in series with each other.
Dialogue: 0,0:00:24.39,0:00:32.24,Default,,0000,0000,0000,,The equivalent impedance Z equivalent\Nis just equal to Z_1 plus Z_2.
Dialogue: 0,0:00:32.24,0:00:35.04,Default,,0000,0000,0000,,So Z_1 equals 3 plus J_2.
Dialogue: 0,0:00:35.04,0:00:39.05,Default,,0000,0000,0000,,Three being the real part sometimes\Nreferred to as the resistance,
Dialogue: 0,0:00:39.05,0:00:45.28,Default,,0000,0000,0000,,and J_2 the imaginary part also\Nsometimes referred to as the reactants.
Dialogue: 0,0:00:45.28,0:00:49.84,Default,,0000,0000,0000,,A second impedance Z_2 equaling 5 minus J,
Dialogue: 0,0:00:49.84,0:00:52.49,Default,,0000,0000,0000,,then the equivalent impedance of\Nthose two connected in series
Dialogue: 0,0:00:52.49,0:00:57.96,Default,,0000,0000,0000,,will simply be 3 plus J_2 plus 5,
Dialogue: 0,0:00:57.96,0:01:02.26,Default,,0000,0000,0000,,minus J, which equals 3 plus five is 8.
Dialogue: 0,0:01:02.26,0:01:07.38,Default,,0000,0000,0000,,J_2 minus J_1 is plus J.
Dialogue: 0,0:01:07.38,0:01:09.71,Default,,0000,0000,0000,,That's its rectangular form,
Dialogue: 0,0:01:09.71,0:01:12.52,Default,,0000,0000,0000,,and we can also write\Nthat it is parallel form,
Dialogue: 0,0:01:12.52,0:01:18.58,Default,,0000,0000,0000,,which would give us then\N8.06 for the magnitude E to
Dialogue: 0,0:01:18.58,0:01:24.99,Default,,0000,0000,0000,,the J at 7.103.
Dialogue: 0,0:01:24.99,0:01:27.88,Default,,0000,0000,0000,,All right, now let's look\Nat these two in parallel.
Dialogue: 0,0:01:27.88,0:01:32.22,Default,,0000,0000,0000,,In parallel, it turns out that as\Nit was with resistance is also
Dialogue: 0,0:01:32.22,0:01:38.58,Default,,0000,0000,0000,,1 over Z_eq is equal to 1 over Z_1,
Dialogue: 0,0:01:38.58,0:01:42.75,Default,,0000,0000,0000,,plus 1 over Z_2.
Dialogue: 0,0:01:42.75,0:01:45.73,Default,,0000,0000,0000,,Now, sometimes we refer\Nto instead of impedances,
Dialogue: 0,0:01:45.73,0:01:53.33,Default,,0000,0000,0000,,we'll refer to admittances where admittance\Nis called y is equal to 1 over Z.
Dialogue: 0,0:01:53.33,0:02:04.17,Default,,0000,0000,0000,,So in this case, we could say then\Nthat Y_eq equals Y_1, plus Y_2.
Dialogue: 0,0:02:04.54,0:02:08.72,Default,,0000,0000,0000,,All right. Let's just simplify\Nthis in terms of impedances.
Dialogue: 0,0:02:08.72,0:02:11.85,Default,,0000,0000,0000,,We know then that 1 over Z_eq.
Dialogue: 0,0:02:12.94,0:02:15.53,Default,,0000,0000,0000,,We need to combine these two terms to get
Dialogue: 0,0:02:15.53,0:02:18.21,Default,,0000,0000,0000,,the common denominator or to get\Na common denominator to combine them.
Dialogue: 0,0:02:18.21,0:02:22.06,Default,,0000,0000,0000,,So it would be the common denominator\Nwould be Z_1 times Z_2,
Dialogue: 0,0:02:22.06,0:02:26.52,Default,,0000,0000,0000,,and in the numerator\Nwould have Z_2 plus Z_1.
Dialogue: 0,0:02:27.56,0:02:31.20,Default,,0000,0000,0000,,Thus that now we can invert them,
Dialogue: 0,0:02:31.20,0:02:38.70,Default,,0000,0000,0000,,and we get Z_eq is equal\Nto Z_1 Z_2 over Z_1,
Dialogue: 0,0:02:38.70,0:02:41.03,Default,,0000,0000,0000,,plus Z_2 or the
Dialogue: 0,0:02:41.03,0:02:43.85,Default,,0000,0000,0000,,product of the impedances divided\Nby the sum of the impedances.
Dialogue: 0,0:02:43.85,0:02:47.57,Default,,0000,0000,0000,,I'll leave it to you to go ahead\Nand plug in Z_1 and Z_2 on these,
Dialogue: 0,0:02:47.57,0:02:51.90,Default,,0000,0000,0000,,but let me just give you that\Nfor these values of Z_1 and Z_2,
Dialogue: 0,0:02:51.90,0:02:54.73,Default,,0000,0000,0000,,we get Z_eq is equal to
Dialogue: 0,0:02:54.73,0:03:04.64,Default,,0000,0000,0000,,2.2 plus 0.6J in rectangular coordinates,
Dialogue: 0,0:03:04.64,0:03:07.04,Default,,0000,0000,0000,,and in parallel coordinates that turns
Dialogue: 0,0:03:07.04,0:03:09.52,Default,,0000,0000,0000,,out to be around a site\Nin polar coordinates.
Dialogue: 0,0:03:09.52,0:03:14.63,Default,,0000,0000,0000,,That turns out to be 2.28 e to
Dialogue: 0,0:03:14.63,0:03:23.10,Default,,0000,0000,0000,,the positive J15.3 degrees.