How powerful is my cooktop?

Beginning cooks often ask for the "temperature" they have to use to cook their food. What matters in reality is not the temperature, but the speed of heat transfer. And that is dependent on a lot of variables: type of food, amount of food, how much is it piled, pan size, pan material, and of course how much energy your stove is pumping out, which is correlated (but not 1:1) to how much energy your stove is consuming from the power socket or gas pipe. Aside from a narrow choice of pans, the only thing you can control during cooking is the amount of energy your stove consumes.

So, you could look up the BTU, but it won't tell you much. You can try turning the knob to the middle, but that rarely produces a medium heat, because all the other variables would have to be right. In the end, there is no "medium heat" stove setting. What people mean when they say "medium heat" is the setting in which the food happens to cook in a certain way, between searing and stewing in its own leaking juices which don't manage to evaporate in time. If you are talking liquid instead of dry pieces, it is the heat which can sustain a strong simmer or slow boil. It takes a bit of experience to recognize when it is happening.

The "food gets done in 10 instead of 5 minutes" is irrelevant. First, the time can vary with variables you have no control with. Second, recipes give bad timings for a plethora of reasons. Some have a wrong feeling of how long it takes and jot it down, others may have timed it for a smaller portion, third can have literally been told by the marketing department to round down aggressively, fourth may do it because a myth has been established and they believe it more than their own experience (see the infamous Slate complaint on caramelized onions). Whatever the reason, the times given in a recipe don't matter much. You recognize that your food is cooking at the correct speed if its state is changing the way it should (which requires some experience) and that it is ready by noticing that it has reached its desired state (which requires either experience or a thermometer).

So, the conclusion: your cooktop has the proper power for home cooking - basically all cooktops sold to home cooks do. You simply need to turn the knob until the food is cooking the way it should, regardless of any considerations about how much it should be turned or how long your food should be taking.

Every stove is different, as you've discovered, and each cookbook author even has a different idea of what "medium" should be since these are by no means standardized measures. You'll just need to adjust, using visual cues (like your oil shimmering) to know when the pan is hot enough, and paying more attention to the recipe's intended result than the sample cooking time.

An illustration, testing on 7 different stoves:

http://www.cooksillustrated.com/how_tos/6623-heat-settings-vary-on-stovetop-burners

In the test kitchen we tested burners on seven different gas stoves set to high heat to see how long it would take a 10-inch disposable pie plate filled with 16 ounces of room-temperature water to come to a boil. For each test we started the timer when the gas was lit. The results? Wild variation. The shortest amount of time it took for the water to boil was 2 minutes and 43 seconds. The longest was 3 minutes and 50 seconds. It seems safe to assume that different stoves would vary on other settings as well.

The vagaries of heat output from stove to stove are the reason we include a time range in our recipes and give visual cues for determining when food has reached the desired stage. It’s much easier to see the changes in your ingredients as they cook than to guess the exact heat output of your burner.

So, what I'd suggest is that you do some real-world calibration. For instance, a recipe starts with a simple sautee of some diced onions over medium heat. The onions should be softened and just beginning to brown, about 7 minutes. If your stove gets the onions to that stage in 4 minutes on medium, then you know your "medium" is quite a bit hotter than what the publisher is expecting and you can adjust either time or temperature accordingly on the rest of their recipes.