What is the name of your state? NJ
Can a circuit board I created be granted copyright protection under the visual art category?
Generally yes, but the protection only extends to the "creative" aspects of the board. In other words, if your board is really the only way to create a circuit board for your particular circuit, then the entire board might be considered "functional" and therefore not subject to copyright protections; however, if your layout is just one particular layout of many that might work, then it is generally protectible by copyright.
This is a tricky area, since expression and functionality often overlap in such a product, and if they overlap too much, functionality wins and no copyright protections exist.
Now, if this were a mask used in a semiconductor chip, then it would clearly be protected because there are specific statutory provisions for maskworks -- but I am not aware of any caselaw that has extended maskwork protections to circuit boards in general, so you need to rely on the more general -- and, unfortunately for you, less protective -- regular copyright statutes.
