WEBVTT NOTE Series and Parallel 1 00:00:00.000 --> 00:00:17.034 Two sentences that generate every rule. Series: one path. The same current flows through everything, and the voltage divides. Parallel: one voltage. Everything sees the same voltage, and the current divides. 2 00:00:17.034 --> 00:00:32.669 The pool asks these directly, in which type of circuit is the current always the same through all components? (series) and in which type is the voltage always the same across all components? 3 00:00:32.669 --> 00:00:37.360 (parallel), and every combination rule follows from them. 4 00:00:37.360 --> 00:01:00.451 Combining resistors. In series, resistances add: R total equals R 1 plus R 2 plus times s Two resistors in series carry the same current, so their voltage drops add, so by Ohm's law their resistances add. 5 00:01:00.451 --> 00:01:04.639 100 Ω and 220 Ω in series give 320 Ω. 6 00:01:04.639 --> 00:01:30.560 In parallel, conductances add, which comes out as the reciprocal rule: (1) divided by (R total ) equals (1) divided by (R 1 ) plus (1) divided by (R 2 ) plus times s 100 Ω and 220 Ω in parallel give 1 / (1/100 + 1/220) = 68.75 Ω. 7 00:01:30.560 --> 00:01:54.946 Two shortcuts worth having. Equal resistors in parallel: the total is one resistor divided by how many there are. Two 100 Ω in parallel is 50 Ω; four is 25 Ω. Two resistors in parallel: product over sum. 8 00:01:54.946 --> 00:02:07.800 (100 times 220) / (100 + 220) = 22000 / 320 = 68.75 Ω. Faster than the reciprocal form for the common case. 9 00:02:07.800 --> 00:02:25.509 The check that catches every error. A parallel total is always smaller than the smallest branch. If you compute two resistors in parallel and get something larger than either one, you have inverted something. 10 00:02:25.509 --> 00:02:43.814 This check costs a second and catches the most common arithmetic slip in the whole subject. Where the pattern breaks: capacitors. Resistors and inductors follow the same pattern, series adds, parallel is reciprocal. 11 00:02:43.814 --> 00:03:02.290 Capacitors are the reverse: Component, Resistors; In series, add; In parallel, reciprocal. Component, Inductors; In series, add; In parallel, reciprocal. Component, Capacitors; In series, reciprocal; In parallel, add. 12 00:03:02.290 --> 00:03:18.807 This is a favourite exam trap and it is not arbitrary. Capacitance grows with plate area, so wiring capacitors side by side (parallel) is effectively building one bigger plate, capacitances add. 13 00:03:18.807 --> 00:03:26.299 Stacking them in series is like increasing the plate spacing, which reduces capacitance. 14 00:03:26.299 --> 00:03:38.752 Reading a real circuit. Real circuits are neither purely series nor purely parallel; they are series and parallel sections nested inside each other. 15 00:03:38.752 --> 00:03:55.327 The method is always the same: Find the innermost group that is clearly one or the other. Reduce it to a single equivalent value. Redraw with that value in place. Repeat until one resistor remains. 16 00:03:55.327 --> 00:04:09.968 There is no shortcut past this, and there is no need for one, each step is either an addition or a product-over-sum. Check yourself. Three 300 Ω resistors in parallel. Total? 17 00:04:09.968 --> 00:04:21.579 A 50 Ω and a 50 Ω resistor in series, that pair in parallel with another 50 Ω. Total? Two 10 µF capacitors in parallel. Total capacitance? 18 00:04:27.579 --> 00:04:50.816 Equal resistors in parallel: 300 / 3 = 100 Ω. The series pair is 100 Ω. In parallel with 50 Ω: (100 times 50) / 150 = 33.3 Ω. Smaller than 50, as required. Capacitors in parallel add: 20 µF. 19 00:04:50.816 --> 00:05:01.823 Before we finish, here are the pool questions this lesson covers, in the exam's own words. 20 00:05:01.823 --> 00:05:08.795 Question. In which type of circuit is the current always the same through all components? 21 00:05:09.695 --> 00:05:12.650 Answer. Series. 22 00:05:13.250 --> 00:05:21.050 Question. In which type of circuit is the voltage always the same across all components? 23 00:05:21.950 --> 00:05:24.630 Answer. Parallel.