Question

A step up transformer converts a low input voltage into a high output voltage. Does this violate the law of conservation of energy??

Answer 1

No, law of conservation of energy can't be violated . As for the transformer ,the input and output power remains the same , so when the voltage is increased in a step up transformer the current supplied at the ends drops , thus maintaining input and output power constant. As power is energy per unit time and is same for both the ends, so, law of conservation of energy is not violated here.
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