"capacity of a" is correct and can be used in written English.
You can use it when you are talking about a thing's ability to contain or hold something. For example, "The capacity of a water bottle is 500 ml."
Mr. Kingman worked mainly in the capacity of a lobbyist.
The middle brother, Joseph Jr., has the mental capacity of a 9-year-old, Ludwik said.
Fully fuelled it had the explosive capacity of a small nuclear weapon.
The plants have an annual production capacity of a combined 815,000 tons of chlorine.
All of these schemes might seem beyond the capacity of a street gang graduate.
A telephone company's copper wires simply cannot compete with the sheer capacity of a cable system.
And, usually, I take pleasure in the capacity of a song to say what I cannot.
EVER wonder why the audio capacity of a standard compact disk is 74 minutes?
Grantors should acknowledge the capacity of a seasoned scientist to leap to new insights.
No offspring would be produced and the productive capacity of a female insect would be lost.
