RewriteRule without absolute path

RewriteRule without absolute path

I want to make this url point to another url in the same directory but I
can't get it to work without giving the absolute url.
I want this url http://www.mysite.com/path/file/
To point to: http://www.mysite.com/path/file.php
I have this: RewriteRule ^(\w+)/?$ /path/$1.php
I want this: RewriteRule ^(\w+)/?$ $1.php
So it should automatically infer that the url should point to a file with
the same name in the same directory. Is it possible?