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I read that increased temperature increases the resistance because the lattice of metal ions (if we're talking about a wire) vibrates more and so more collisions occur between the electrons and the ions, thus increasing resistance.

However, on reading up about internal resistance, many websites were saying that increased temperature decreased the internal resistance. For example: https://www.vedantu.com/question-answer/effect-of-temperature-on-internal-resistance-of-class-11-chemistry-cbse-5fb601994886f710fc005d1f

Why are the relationships between temperature and resistances different?

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There exist both kinds of resistors, so called thermistors it is easiest to read it up in https://en.wikipedia.org/wiki/Thermistorhttps://en.wikipedia.org/wiki/Thermistor the article you linked is about batteries, so liquid resistors you can not compare with metallic conductors.

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