I asked essentially that same question some time ago, here: “Has a value of” vs. “has the value of”. What I've learned since then is approximately the following.
There is one unfortunate truth to keep in mind whenever English articles are discussed, and it is this: there is no completely general and reliable algorithm for figuring out which article (if any) is needed. On the contrary, it seems that the English system of articles has quite a bit of instability. In particular, there are many instances of article use that do not seem to be deducible from any general principles—something that becomes especially obvious in cases when there is a difference between British and American usage. So for example, when we want to say that someone has been hospitalized, in British English you'd say he's in hospital, whereas in American English you'd say he's in the hospital, even though you don't have a particular hospital in mind (see here). And there is no general principle that would explain why it's OK to say she has the flu even though we don't have any particular kind of flu in mind, but under the same conditions, it's not OK to say *she has the influenza (you must say she has influenza instead). As Janus Bahs Jacquet said in a comment to this question, 'Articles are a fairly random part of any language that has them: they pop up in places where you’d never expect them, and they’re conspicuous in their absence in places where you’d never dream of not seeing them. Their use is, to a certain extent, outside the normal logic of the grammar of a language, and their idiosyncracies must be learnt by rote.'
Now, as far as the particular construction you're asking about. It's a special case of the following construction: [measurable quantity] + of + [numerical quantity]. Other examples would be speed of, value of, price of, … And it is just a fact of English that before such a construction, you use the indefinite article:
The electric field within the capacitor has a value of 170 N/C.
The Commodore PET was also released in 1977 with a price of $800.
The front of the train has a speed of 23 m/s.
There does not seem to be a general principle that would allow you to deduce this rule. But it is a rule of English all the same.
So striving for completely general rules is probably hopeless. Nevertheless, there are some more restricted situations where some rules (or at least strong tendencies) may be discerend. Concerning preposition phrases with of, two such strong tendencies are described in the following section of Collins COBUILD English Guides: Articles (pp. 30-31):
4.10 Nouns qualified by an 'of'-phrase
There are two cases where an 'of'-phrase after a noun suggests a unique interpretation and so normally requires the definite article.
Firstly, where the noun involved refers to an action, event, or state and the 'of'-phrase indicates the performer of the action or the thing affected:
..following the closure of a Courtaulds factory.
Orders should not be cashed after the death of the person.
...the elimination of low pay.
Here the first nouns refer to (possible) actions or events, and can be related to verbs: a factory was closed, the person died, low pay was or will be eliminated.
Secondly, certain nouns which refer to a part or characteristic of
something are followed by an 'of'-phrase very frequently, and have unique reference.
...after the beginning of the tax year.
The price of copper fell spectacularly.
...Picture 5 at the top of page 43.
...at the end of 1980.
The tax year has only one beginning, copper has only one price, page 43 has only one top, 1980 has only one end. Here are some nouns like this.
back end middle top
beginning front price weight
bottom height size
edge length title
Note that you can also use the definite article before these nouns even when they are not qualified because they are often found in association with other nouns which have been mentioned before.
A generalization of the above is given in another section of the same book (p. 30):
4.9 Nouns with qualification
The definite article is also used with nouns when it is the phrase or
clause following the noun (rather than a previous word or the general
situation) which indicates which thing the noun refers to. Nouns with
phrases or clauses after them are said to be qualified.
It is the title of the chapter
...haunted by the fear that no one would turn up.
Nouns can be qualified in a number of ways:
• by prepositional phrases:
The only way to learn the price of something is to pay for it.
The reason for this selection is obvious.
...on the basis of the data in Table 7.l.
Of course he knew the answer
to that one.
The preposition most commonly used in these phrases is 'of': see
section 4.10 [above!].
• by relative clauses:
What about the argument that reality isn't like that?
…the amount it cost to build the house.
…to get back to
the hotel where he was staying.
…the success which has been achieved.
• by clauses with non-finite verbs (that is, infinitives or
Power at work is the power to get decisions implemented.
…the interest paid on overdrafts and credit cards.
• by apposition (using one noun group to qualify another)
And he wrote a book with the title 'The Summing Up'.
Note that when uncount nouns referring to qualities or feelings are
used with the, it is usually because they are qualified.
I tried to concentrate on the beauty of the scenery.
I share the anger that many of you must feel.
This leaves us with a practical question for non-native speakers: how does one figure out which article (if any) to use in any particular instance one is unsure of? There is only one answer: look at patterns of usage by native speakers. These days this can be done very effectively with the help of google books. Try googling the exact phrase you need, in all variations, and see if any patterns emerge. The patterns I'm talking about include the context in which the phrase appears. Play with the phrasing, modify a bit if need be.
And if no clear pattern emerges, this may well be because different native speakers would make different choices on that issue. In that case, it probably makes no difference (as far as acceptability) what choice you make.