Error while adding Site columns (fields) to list content types

Recently, I had a situation where I need to add site columns (available in root web) to a content type reference in a particular list under a particular web.

I wrote the code below 

var field = web.Site.RootWeb.AvailableFields[new Guid("<<FieldID>>")];
foreach (SPContentType cType in web.Lists["ListName"].ContentTypes)
{
    cType.Fields.Add(field);
    cType.Update();
}

but it was not working as expected and throwing the below exception

"This functionality is unavailable for field collections not associated with a list."

After some research, I came to know that the field needs to be added as a SPFieldLink and not as SPField itself since the field already exists in the root web. The below modified code is working fine for me.

var field = web.Site.RootWeb.AvailableFields[new Guid("<<FieldID>>")];
foreach (SPContentType cType in web.Lists["ListName"].ContentTypes)
{
    SPFieldLink fieldLink = new SPFieldLink(field);
    cType.FieldLinks.Add(fieldLink);
    cType.Update();

}

Hopefully this helps some one or may be myself in the future when I struggle with the same issue.

Thanks

Senthil S