I recently learned that capacitors have two sides that are interchangeable, meaning you can hook them up to a battery in either configuration. If this is true, can you just hook both sides up to a positive terminal?
Here's a quick hands-on lesson in what capacitors do:
Get yourself an electrolytic capacitor with a value of 10 or more microfarads (uF,mfd). Any voltage rating (WVDC) will do.
Connect the capacitor momentarilly to a standard D-cell, C-Cell or AA-Cell battery with the cap's negative lead connected to the negative terminal of the battery and the cap's positive lead to the battery's positive terminal. There's no danger here because of the battery's low voltage, do it with your bare hands. (Don't try this barehanded with any other voltage source besides a single cell battery !!!)
Quickly connect the capacitor to a DVM or analog voltmeter. You will see that the capacitor now has a voltage across it. If you watch the DVM you will see that this voltage slowly decays until it is finally reduces to 0 volts. That's what a capacitor does, plain & simple, it stores voltage.
More accurately, the capacitor stores electrical energy in the dielectric material between its internal plates. Problem is, we don't have instruments that measure "electrical energy" directly, but we do have instruments that measure voltage ( e.g. your DVM ). The voltage you measure is indicative of the energy stored in the capacitor.
The bigger the capacity of your capacitor (i.e. more microfarads) the more energy it will store. In the above demonstration, if you have a small cap and a large cap, they will both charge to the same voltage when you touch them to the battery (1.5 volts or so), but the larger cap will take longer to discharge to 0 volts.
As a convenience you can connect the DVM to your capacitor's leads directly with clip leads, and leave them connected as you touch the capacitors leads to the battery's terminals in the correct polarity. Then release the battery from the capacitor leads and watch what happens.
Now try touching both leads to just one terminal of the battery as you asked in your original question. Tell me what you observe.
You could think of capacitors in 2 ways. The first is that in a purely DC path all they do is block current (once they have fully charged to the voltage across them).
In an AC signal path they are more like a variable resistance, and the term for it is capacitive reactance, which is measured in ohms and changes with frequency and capacitance which is measured in Farads ( uF = microFarads ). Wiki has a good definition of a Farad.
Capacitors are primarily filters and can be made from many types of dielectric material. Meaning insulators basically.
If by conduct you mean exchange electrons from one side to the other, then yes capacitors can "conduct" on both sides because AC current goes in both directions but for DC they don't "conduct" at all!
capacitors have two sides that are interchangeable
Some capacitors, but not all, are unpolarised. meaning they work the same no matter which way around you connect them. However some capacitars are polarised, notably Electrolytic capacitors. These capacitors will usually be damaged if you connect them the wrong way around.
Note that this need to be connected the correct way around is a disadvantage, it is not (usually?) a feature that is exploited in a circuit design. Engineers only put up with this awkward characteristic because there's no other cost-effective alternative construction for capacitors with high values of capacitance (Farads).
you just hook both sides up to a positive terminal
You could do that with any capacitor, but it wouldn't perform any useful purpose.
For a capacitor to perform a useful purpose, at some point in it's operation there has to be flows of energy into and out of it. That flow implies that, during the flow, there will exist a measurable voltage between/across the two terminals.
Yes; however, with some capacitors (like electrolytics) they will explode if you wire them in reverse. Ceramics and other small capacitors should work fine. I have a few weird capacitors I can't really identify that seem to have different capacitances depending on their polarities, but this has all been based on personal observation, and these were very strange capacitors.