Those input power and voltages are rated input power and voltages.
For example you can drive electric motors over rated power but they will get too hot and eventually break. There are also electric motor duty classifications for industry.
See this for short introduction:
http://www.electricalengineering-book.com/duties-of-induction-motors.html
In practice this means that one same machine could be used for two different applications.
For constant non-stop usage rated power can be e.g 100 W but then for cyclic usage where motor stops e.g for 5 minutes and then drives for 2 minutes the rated power can be e.g. 130 W.
This was just an illustrative example from industry machines but I have not checked how big difference in power output there actually is between these two types.
Back to this case:
Peltier element's rated input power in this case is that around 96 W. You can also use it with lower power. For example you could attach a sensor system that measures temperature of cooled object and then the input power is adjusted by control circuit to adjust for example voltage given to the element. Since peltier is a semiconductor device it is likely more prone to break with over-rated power even for short times. I do not recommend trying that.
The rated numbers for that element can be based on theory and then it is tested properly to be sure that it works under that load for long time enough to be sold for consumers.
Also shortly about fundamental theory:
- Voltage (potential difference between two planes, nodes... etc.) produces electrical current -> resistance limits current -> power is consumed to that resistance to get over it. Refer to Kirchhoff 1st and 2nd and Joule's law.
In practice you can buy cheap multimeter, small battery and a small resistive lamp, couple of resistors and see with measurements when you change resistance in that circuit and see in practice in brightness of the lamp. This is brilliant way of getting started in practice.
Remember to stay safe while measuring and do not measure any high power device voltages or currents if YOU are not familiar with the theory of electric laws! Small 9 V alkaline batteries are safe enough but things get much more dangerous even with 12 V car batteries if you don't know what you are doing!
Cables don't just have resistance, they have inductance. You've acccidentally built a boost converter; you have an LC circuit which is resonant at about the width of your pulse.
If you want to measure the resistance of the cable, use DC. Measuring the characteristic impedance is more complicated. Is that what you actually want.
Best Answer
According to a reference from the Handbook of Electronic Tables and Formulas for American Wire Gauge a conservative estimate for 24AWG power transmission is 0.577 amps. Current-wise, I'd expect you to be fine. I'd still recommend testing it and monitoring the temperature for a while to make sure. If you've got that cable in a tight bundle of some kind, it will get warmer than if it was in free space. On the bright side, wire that small won't take long to reach its ultimate temperature!
As for voltage drop, according to this AWG table, 60 meters of 24AWG has a resistance of about 5 ohms. 500 mA will drop 2.5V over that distance. You also have to consider that the current has a return path, so that's 2.5V drop in each of the positive and negative legs, 5V drop total.
If, on the other hand, the draw is on the low end of your spec, you'll only get 3.5V drop total. That means that the voltage on your load (the Raspberry Pi) will vary by 1.5V depending on how much current it's drawing. That's quite some variation, and you'll need to make sure it can handle that.
If it was me, I'd come up with a different plan. You're running really close to the edge of what's reasonable.