PerryBebbington:
Yes, DC doesn't go through capacitors. The capacitor is in the right place as far as I can tell. It's job is to smooth the output from the rectifier and it should always be connected. Unless we are talking about different capacitors it's called a smoothing capacitor.I was so focused on how you were supplying power I didn't notice PWM to the relay. No, you can't do that, a relay cannot switch anything like fast enough for normal PWM. There is an exception, which I am pretty sure does not apply here. For a heating load you might want PWM running very slowly. My heating controller uses PWM but the time for 1 cycle is 12 minutes. That is unusual for PWM.
Hmm not even if I use a solid state relay? Any recommendations besides PWM? In this instance I was going to start with an incandescent light bulb. I've done triac control on a bulb but I wanted to see if DC is generally better and easier to control. I'll be using a potentiometer to check but I eventually want to be able to program my own PID controllers for various things like temperature, motor speed, etc.