Winning the exchange through a pin!

Again a few puzzles but this time forks arent in the spotlight. This time it's the so-called 'pin'. A pin is a situation brought on by an attacking piece in which a defending piece cannot move without exposing a more valuable defending piece on its other side to capture by the attacking piece.

Allow me to demonstrate. In the next diagram the rook is pinned because if it moves it will expose the king. So no matter what black does, he will lose it's rook.

And now it's pin-puzzle time. Have fun!

The next one is a little harder:

If you wondered why the king moved you should look at this one, same concept except the king doesn't move this time.

Another variation:

A fresh puzzle:

The hardest: