Originally Posted by Tphage

I was once a high school Physics teacher so hopefully I will steer you on a righteous path. Just before we get to your questions, can I give you a little information, which is actually extremely important that you understand, if you are going to really get into electric power and you want to end up building your own models, and choosing suitable electric motors, esc's and batteries yourself ( rather than just buy RTF or ARF's with them already installed ) or else just using what someone else tells you they use. I am actually a bit unsure of your knowledge level. Apologies if you already know this !

Of the three components (motor, esc, battery), the current is drawn by the motor, the maximum value being determined by the motor's resistance and the battery's voltage. The esc "current rating" and the battery "current rating" do NOT determine the current flow in the circuit. Those ratings are just maximum safe values for those components, not to be exceeded. You have to make sure that the esc's current rating and the battery's current rating ( what you talked about in your post ) are high enough to cover the motor's demands i.e. at least as high as the max. current draw of the motor, but preferably a little higher to give you some safety margin. About 20 % higher works about right.

If you are setting up your own system from scratch, you always start with choosing the motor ( that's another topic ). Then you can select a suitable battery cell count / voltage to power the motor. Then you figure out the MAXIMUM current this motor will ever draw (which is highly dependent on propeller choice and throttle setting). Then you choose the esc current rating and the battery current rating to match.

An example: If a motor decides it wants ( draws ) a maximum of 40A, then you must use at least a 40 A rated esc and at least a 40 A rated battery ( continuous discharge rating, not burst rating ). But since you should factor in a safety margin, it's much better to use a ( say ) 50 A esc and a 50 A battery ( continuous rating ) with a 40 A motor.

In other words, the esc current rating and the battery current rating can be about the same, but should be about 20 % higher than the max. current the motor will ever draw.

Now to your questions ( bear in mind I am not sure if you have chosen the motor or it's what was factory installed. I don't know the Conscendo. But it makes no difference to what I have written. )

If I have a 1500 mah LiPo that has a rating of 25c, my understanding is that it can deliver 37.5 amps continuously because the formula (I think) is 1.5 amp-hours x 25c = 37.5 amps.

That is totally correct.

if my Conscendo has a 30-amp ESC, does that mean that as long as my LiPo can deliver 30 amps, I am OK?

If your esc was chosen correctly, the answer is yes.

But if my ESC is a 30 amp unit, does that means 30 amps is the max anyway that my motor can draw?

If your esc was chosen correctly, the answer is yes. ( Bearing in mind the 20 % thing. So the motor should really draw no more than say about 25 A. )