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I found this on Wikipedia:
(in the IV. Finale section)
1 has four crotchets;
2 has two crotchets and one minim
3 has one and a half crotchets, one quaver, and one minim
The total duration of each bar is different from each other. So what is the time signature? Shouldn't they be all equal?
Your question isn't really "what is the time signature" but how to add up the durations of note rhythm values.
The time signature of the example is 4/4 and so there will be 4 quarter notes per measure.
For this passage the simplest thing to do is count up duration using the smallest unit of rhythm value which in this case is an eighth note.
BASIC NOTE VALUES 1 eighth note (quaver) = 1 eighth note 1 quarter note (crotchet) = 2 eighth notes 1 dotted quarter note = 3 eighth notes 1 half note (minim) = 4 eighth notes VALUES AND DURATION OF EACH MEASURE m.1 1 quarter note = 2 eighth notes 1 quarter note = 2 eighth notes 1 quarter note = 2 eighth notes 1 quarter note = 2 eighth notes -------------------------------------- total 8 eighth notes m.2 1 half note = 4 eighth notes 1 quarter note = 2 eighth notes 1 quarter note = 2 eighth notes -------------------------------------- total 8 eighth notes m.3 1 dotted quarter note = 3 eighth notes 1 eighth note = 1 eighth note 1 half note = 4 eighth notes -------------------------------------- total 8 eighth notes
You could also add up durations using quarter note = 1, but then you would need to use values like dotted quarter = 1.5 and eighth = 0.5 and that seems a bit more difficult than adding whole numbers.
With a time signature of, say, 4/4, it does not mean every bar must have 4 crotchets (1/4 notes). How could it? It would be a very boring piece rhythm-wise!
Each of those bars posted actually has the equivalent of 4 crotchets, and that's what counts - literally. The time signature tells how many of what, admittedly. But there are many combinations of notes which can be, and are, used to fill each bar - including rests. And once a time signature is stated, the writer is duty bound to keep to it, or change to a different time signature if the last one is inappropriate, which happens, although not that often in 'Classical' music, at least
So, this question is actually asked using false premises, but hopefully this answer will explain why.
EDIT: I guess you're considering the 4th movement, which has a time signature of 'C'. That in fact, is another way to designate 4/4, which may be where the confusion comes from?
Mathematically, we can say it's in either 4/4 or 2/2 time, sometimes marked as 𝄴 (common time) or 𝄵 (cut time) respectively. (There are other esoteric possibilities, but let's keep it simple). If we look at the actual score, we can see that Beethoven chose 𝄵.
You say "The total duration of each bar is different from each other." You are mistaken. Minims are worth two crotchets, a dotted crotchet is one-and-a-half, a quaver is a half. So each bar adds up to four crotchets.
Think of it like (British) money. 4p can be 4x1p, 2x2p, 1p+1p+1½p+½p, or a 4p piece (OK, I know we don't have ½p coins any more, or a 4p piece, but you get the idea!)
C.
Actually all measures have the same length. The notes use the time differently in every measure, but they add all up to 4/4.
