The BR tag does NOT add a new blank line. It mearly breaks a line of text into two lines. Since you don't have any text after the BR, nothing will happen.
Think of this way. Any text you have between P tags will be one single line of text in HTML. In your sample code, it actually looks like this:
<p>This is the first</p><p>This is second</p>
Since the paragraph tags break the text and inserts blank space between paragraphs, there is nothing visible for the BR tag to do. Without the BR tag, you'll get a single blank line between the paragraphs.
Perhaps you're looking to put the BR between the paragraphs?
<p>This is the first</p><br><p>This is second</p>
This is add extra space between the paragraphs.