Imagine I have a simple AC generator. I am providing energy to rotate the coil, which converts this to electrical energy. If I connect the ends to an electrical component such as motor, bulb, the power consumed would be equal to $P=V^2/R.$ Now if I instead connect the ends to a low-resistance component, the power consumed would increase, meaning that I would have to apply more power to rotate the coil at the same speed. What am I missing here?