I have an Arduino uno that I am powering through a USB cable. I would like to connect a cable to the barrel jack in order to draw 5V and 20 mA. Currently, it seems I cannot draw any current through the barrel jack even though I am measuring a voltage difference. However, I am using a center negative cable; is this that would simply be resolved by switching to a center positive cable. or is the uno not capable of doing what I am asking?
Use a center positive power supply. Using the wrong polarity can destroy chips. Fortunately the Uno has a diode in the ciruit it to protect against exactly this kind of thing.
Why do you require the barrel jack to grab 20mA at 5V when you can use the usb connection and get that 20mA from the 5V pin? The onboard regulator is more than capable of supplying that small amount of current.
I would like to connect a cable to the barrel jack in order to draw 5V and 20 mA.
The barrel jack is for powering the Arduino, you can not draw power from it. This is because their is a series diode and this stops any current flow. The voltage you can measure is simple the reverse leakage current of that diode.
If you want 5V to power something then use the 5V pin.