1
00:00:00,424 --> 00:00:01,692
- [Voiceover] Now we're
ready to start hooking up

2
00:00:01,692 --> 00:00:06,111
our components into circuits,
and one of the two things

3
00:00:06,111 --> 00:00:09,583
that are going to be very useful
to us are Kirchhoff's laws.

4
00:00:09,583 --> 00:00:11,279
In this video we're gonna talk

5
00:00:11,279 --> 00:00:13,779
about Kirchhoff's voltage law.

6
00:00:15,978 --> 00:00:17,073
If we look at this circuit here,

7
00:00:17,073 --> 00:00:21,240
this is a voltage source, let's
just say this is 10 volts.

8
00:00:22,862 --> 00:00:24,911
We'll put a resistor connected to it

9
00:00:24,911 --> 00:00:27,662
and let's say the resistor is 200 ohms.

10
00:00:27,662 --> 00:00:31,212
Just for something to talk about.

11
00:00:31,212 --> 00:00:34,497
One of the things I can do
here is I can label this

12
00:00:34,497 --> 00:00:36,354
with voltages on the different nodes.

13
00:00:36,354 --> 00:00:37,876
Here's one node down here.

14
00:00:37,876 --> 00:00:40,987
I'm going to arbitrarily
call this zero volts.

15
00:00:40,987 --> 00:00:43,416
Then if I go through this voltage source,

16
00:00:43,416 --> 00:00:47,166
this node up here is
going to be at 10 volts.

17
00:00:48,959 --> 00:00:50,413
10 volts.

18
00:00:50,413 --> 00:00:52,602
So here's a little bit of jargon.

19
00:00:52,602 --> 00:00:54,739
We call this voltage here.

20
00:00:54,739 --> 00:00:58,411
The voltage goes up as we go
through the voltage source,

21
00:00:58,411 --> 00:01:01,161
and that's called a voltage rise.

22
00:01:04,872 --> 00:01:06,621
Over on this side, if we are standing

23
00:01:06,621 --> 00:01:08,864
at this point in the circuit right here

24
00:01:08,864 --> 00:01:13,351
and we went from this
node down to this node,

25
00:01:13,351 --> 00:01:16,908
like that, the voltage
would go from 10 volts

26
00:01:16,908 --> 00:01:19,059
down to zero volts in this circuit,

27
00:01:19,059 --> 00:01:21,809
and that's called a voltage drop.

28
00:01:24,881 --> 00:01:28,031
That's just a little
bit of slang, or jargon

29
00:01:28,031 --> 00:01:31,410
that we use to talk
about changes in voltage.

30
00:01:31,410 --> 00:01:33,198
Now I can make an observation about this.

31
00:01:33,198 --> 00:01:36,884
If I look at this voltage
rise here, it's 10 volts,

32
00:01:36,884 --> 00:01:41,051
and if I look at that voltage
drop, the drop is 10 volts.

33
00:01:41,899 --> 00:01:44,482
I can say the drop is 10 volts,

34
00:01:45,520 --> 00:01:49,687
or I could say the rise on
this side is minus 10 volts.

35
00:01:50,768 --> 00:01:52,770
A rise of minus 10.

36
00:01:52,770 --> 00:01:56,149
These two expressions mean
exactly the same thing.

37
00:01:56,149 --> 00:01:58,752
It meant that the voltage
went from 10 volts

38
00:01:58,752 --> 00:02:03,078
to zero volts, sort of going
through this 200 ohm resistor.

39
00:02:03,078 --> 00:02:05,054
So I ran a little expression for this,

40
00:02:05,054 --> 00:02:08,554
which is, v-rise minus v-drop equals what?

41
00:02:14,774 --> 00:02:16,483
Equals zero.

42
00:02:16,483 --> 00:02:19,499
I went up 10 volts, back down 10 volts,

43
00:02:19,499 --> 00:02:23,105
I end up back at zero volts,
and that's this right here.

44
00:02:23,105 --> 00:02:26,375
This is a form of Kirchhoff's voltage law.

45
00:02:26,375 --> 00:02:29,287
It says the voltage rises minus

46
00:02:29,287 --> 00:02:32,998
the voltage drops is equal to zero.

47
00:02:32,998 --> 00:02:35,279
So if we just plug our
actual numbers in here

48
00:02:35,279 --> 00:02:38,529
what we get is 10 minus 10 equals zero.

49
00:02:43,556 --> 00:02:44,986
I'm gonna draw this circuit again.

50
00:02:44,986 --> 00:02:46,761
Let's draw another
version of this circuit.

51
00:02:46,761 --> 00:02:50,928
This time we'll have two
resistors instead of one.

52
00:02:57,750 --> 00:02:59,083
We'll make it...

53
00:03:02,266 --> 00:03:05,266
We'll make it two 100 ohm resistors.

54
00:03:09,877 --> 00:03:11,279
Let's go through and label these.

55
00:03:11,279 --> 00:03:13,616
This is again 10 volts.

56
00:03:13,616 --> 00:03:16,659
So this node is at zero volts.

57
00:03:16,659 --> 00:03:18,929
This node is at 10 volts.

58
00:03:18,929 --> 00:03:19,762
What's this node?

59
00:03:19,762 --> 00:03:21,693
This node here is...

60
00:03:21,693 --> 00:03:23,416
These are equal resistors,

61
00:03:23,416 --> 00:03:26,249
so this is gonna be at five volts.

62
00:03:29,077 --> 00:03:32,000
That's this node voltage
here with respect to here.

63
00:03:32,000 --> 00:03:33,833
So that is five volts.

64
00:03:35,499 --> 00:03:37,082
This is five volts.

65
00:03:43,523 --> 00:03:45,446
And this is 10 volts.

66
00:03:45,446 --> 00:03:47,595
So let's just do our visit again.

67
00:03:47,595 --> 00:03:50,786
Let's start here and
count the rises and drops.

68
00:03:50,786 --> 00:03:54,953
We go up 10 volts, then we
have a voltage drop of five,

69
00:03:56,727 --> 00:03:58,891
then we have another voltage drop of five,

70
00:03:58,891 --> 00:04:00,706
and then we get back to zero.

71
00:04:00,706 --> 00:04:02,055
We can write the sum of the rises

72
00:04:02,055 --> 00:04:04,832
and the falls just like we did before.

73
00:04:04,832 --> 00:04:08,999
We can say 10 volts minus
five minus five equals zero.

74
00:04:12,469 --> 00:04:13,302
Alright.

75
00:04:13,302 --> 00:04:14,472
So I can generalize this.

76
00:04:14,472 --> 00:04:18,880
We can say this is general
we can do the summation,

77
00:04:18,880 --> 00:04:20,576
that's the summation symbol,

78
00:04:20,576 --> 00:04:24,743
of the v-rise minus the sum
of the v-fall equals zero.

79
00:04:35,649 --> 00:04:39,668
This is a form of Kirchhoff's voltage law.

80
00:04:39,668 --> 00:04:42,152
The sum of the voltage rises minus the sum

81
00:04:42,152 --> 00:04:45,837
of the voltage falls is
always equal to zero.

82
00:04:45,837 --> 00:04:47,692
There's a more compact way to write this

83
00:04:47,692 --> 00:04:51,885
that I like better, and that
is, we start at this corner...

84
00:04:51,885 --> 00:04:54,876
We start at any corner of the circuit.

85
00:04:54,876 --> 00:04:57,226
Let's say we start here.

86
00:04:57,226 --> 00:05:00,893
We're gonna go up 10
volts, down five volts,

87
00:05:02,098 --> 00:05:03,728
and down five volts.

88
00:05:03,728 --> 00:05:06,946
So what we're adding is the voltage rises.

89
00:05:06,946 --> 00:05:09,850
We're adding all the voltage rises.

90
00:05:09,850 --> 00:05:10,933
Rise plus 10.

91
00:05:12,770 --> 00:05:16,428
That's a rise of minus five
and a rise of minus five.

92
00:05:16,428 --> 00:05:20,595
So I can write this with
just one summation symbol.

93
00:05:22,949 --> 00:05:27,116
The voltages around the
loop, where i takes us all

94
00:05:28,711 --> 00:05:31,794
the way around the loop, equals zero.

95
00:05:33,450 --> 00:05:36,828
So this means I start
any place on the circuit,

96
00:05:36,828 --> 00:05:39,511
go around in some direction,
this way or this way,

97
00:05:39,511 --> 00:05:42,328
up, down, down, and I end up back

98
00:05:42,328 --> 00:05:45,613
at the same voltage I started at.

99
00:05:45,613 --> 00:05:48,530
So let's put a box around that too.

100
00:05:54,652 --> 00:05:57,735
This is Kvl, Kirchhoff's voltage law.

101
00:05:59,992 --> 00:06:01,875
Now I started over here in this corner,

102
00:06:01,875 --> 00:06:02,864
but I could start anywhere.

103
00:06:02,864 --> 00:06:04,699
If I started at the top and went

104
00:06:04,699 --> 00:06:08,032
around clockwise, if I started here say,

105
00:06:10,207 --> 00:06:13,790
I would go minus five,
minus five, plus 10,

106
00:06:15,240 --> 00:06:16,188
and I'd get the same answer.

107
00:06:16,188 --> 00:06:18,257
I'd still get back to zero.

108
00:06:18,257 --> 00:06:21,162
If I start here and I
go around the other way,

109
00:06:21,162 --> 00:06:22,684
the same thing happens.

110
00:06:22,684 --> 00:06:25,267
Plus five rise, plus five rise,

111
00:06:26,542 --> 00:06:28,985
and this is a 10 volt drop,

112
00:06:28,985 --> 00:06:31,348
so it works whichever way
you go around the loop,

113
00:06:31,348 --> 00:06:35,015
and it works for whatever
node you start at.

114
00:06:37,050 --> 00:06:41,126
That's the essence of
Kirchhoff's voltage law.

115
00:06:41,126 --> 00:06:43,460
We're gonna pair this
with the current law,

116
00:06:43,460 --> 00:06:45,996
Kirchhoff's current
law, and with those two,

117
00:06:45,996 --> 00:00:00,000
that's our tools for
doing circuit analysis.