How to connect Smart TV to Time Capsule? I want to be able to copy movies on a Time Capsule and watch them on my Smart TV (Philips 32PFH5500) without the computer on. 

How can I set this up?
Time Capsule shares files via SMB protocol, so if your TV can connect to a networ share, you are good to go.

If your TV cannot do that, you'd have to jailbreak the TC since it doesn't allow running apps or media streaming code out of the box.