If I am designing a new product and want to copyright the circuit, what is the scope of that copyright? Does it include the 'design' part of the circuit or is it just the 'schematic' or 'drawing'?
If the copyright holds only for drawing, what are the ways in which I can protect my 'design'?
You can't copyright a circuit (at least here in the US). Even if you could, someone could just make a small change to the circuit and then the copyright wouldn't apply. You can, however,copyright firmware, etc.
This means unless the circuit has patented blocks, any product as such cannot be copyrighted. In this case, if I have to copyright my product, how can I do it?
You can PATENT a product, or elements of it. Copyright applies more to things like art, writing, etc., things that are authored. Patents are for protecting inventions. You could, I believe, copyright a PCB layout, for example. But I am not a lawyer.