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First of all the power consumed is only dependent on the load (eg. any appliance) connected to the source. A load will always draw its rated power. If you have increased your voltage to twice then the current drawn by the device will become half but the power consumed will remain same.

the power consumed is given by:

P= V*I* cos(fi)

here for a given load P(power), cos(fi) are constants.

Then if V becomes 2V then current will be I/2.

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Q: When voltage across a certain resistance is V the power delivered is P when the voltage is doubled to 2V what is the power?
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