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in terms of Direct current, P=IV. Another form is P=V^2/R. If you are to connect only a single resistor directly to a 1.5 volt battery, you will need a resistor of size 0.45 ohms. Notice though that this is a current draw of about 3.3A. At the typical 2700mAhour rating of AA size battery, it would last (in an ideal world) about 49 min. You will also need some rather large gauge wire to prevent the 3.3A from burning up your wire.

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Q: What Resistor do you need for a 5 watt 1.5 volt alkaline battery?
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