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So, I have a project where I have a bicycle that powers a type of generator. I have everything else done, but I need to pick a generator.

My first problem is that I don't really know which type of generator to use. I am relatively new to electromagnetism, electricity, and engineering in general(I am doing this project by myself, and I am in high school; I do not have a profound background in this type of stuff).

I am debating between using a doubly-fed generator(which is AC), or some type of dynamo(which is DC).

My goal is to charge a relatively large battery. In this regard, which type of generator would be better in terms of general electrical power and cost-effectiveness?

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    $\begingroup$ A dynamo actually generates AC but the commutator does the rectification. $\endgroup$ – Solar Mike Jul 3 '17 at 20:47
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AC generators are simpler. Their inherent construction property is that the sine wave of AC is directly derived from the rotary motion of the rotor. There is no commutator, which is a part that suffers wear over the course of use of a dynamo (a DC generator). Even with a dynamo, the current isn't exactly DC, just an approximation.

Neither is "better" or "worse", they both have their own applications. Digital electronics definitely prefer low-voltage DC. Heavy machinery definitely prefers AC, three-phase. Batteries naturally produce DC while generators naturally produce AC. Transforming between various voltages is possible with very little loss for AC, in a very lossy but very easy way for low-power DC. Rectification (AC->DC) is much easier than changing DC into AC, or changing frequency of AC (by any other means than changing RPM of the generator).

What you should use in your project should primarily depend on what you want to power, and what parts you have at hand. The decision is still yours, but hopefully now you know a little more to make it.

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