You have nearly all the information you need to solve these problems in this web page and in the web pages that are linked from this page. They are hard problems. I would be shocked if any of you could answer any of them.

1. If I have a 1.5 battery with .05 Ohms of resistance inside of it, and I want to choose a resistor to get the maximum amount of energy out of the battery and turned into heat in the resistor, how many Ohms should the resistor be? How much energy is turned into heat in this resistor? How hot does the resistor get? What does the resistor look, smell, and feel like when it gets that hot?

2. What wire size should I use to get the highest NI for a 1.5v battery with .05 Ohm internal resistance, where the coil is two inches tall, one inch in diameter, and is wound around a 1/4" shaft?

3. How long will a D-cell alkaline battery powering the coil in problem 2 last?