Assuming the following phrase is what is intended,...
a state of residual charge of battery of a microphone at a ..
it can be broken into chunks:
[a state of][residual charge of battery][of a microphone][at a...]
First of all, we have all kinds of phrases in which the noun after of does not have an article:
How about a slice of cake? a piece of pie? a bowl of oatmeal? a loaf of bread? a cup of coffee? a lot of money? a ton of bricks? a herd of African cattle? a school of tuna fish? a mountain of homework? a smidgen of truth? a collection of stamps? a peck of pickled peppers? a group of children? A bottle of water? A glass of milk?
Some of the above nouns that follow of are singular count nouns, some are plural count nouns, some are mass nouns. The point is that we do not have to use an article in this kind of construction.
Getting back to your sentence:
[a state of][residual charge of battery][of a microphone][at a..
This is quite awkward; however it works like this one:
[a pile of][leftover change of clothes][of a teenager][at a..
I realise "a pile of leftover change of clothes" is awkward, but then so is the corresponding phrase of the original. The important thing is that
Both change of clothes and charge of battery are a unit.
Like 'bottle of water', 'glass of milk', etc. As we have seen, an article does not have to come after of in this kind of construction.