I'm looking for equations on how to calculate output voltage of a simple power supply made of a step down transformer with Rs secondary resistance, a bridge rectifier and a capacitor with different loads.
Here is a picture of what happens in order to help you find the rest of the formulas: -
It's easy to just let you have all the formulas but it's a learning process best undertaken with half-help. Call me mean if you will.
If Rs is a significant value (not usually that critical to simple power supplies) then you'll need to factor that is but if it's a small percentage of the DC load then ignore for now.
The ripple is not a result of the load resistor but in fact is a result of the capacitor discharging into the load resistor which causes a smoother wave, the larger the capacitor the more negligible the ripple factor but it can be hazardous if too large a capacitor is used if you're looking to build an amplifier