Suppose that the voltage is reduced by 10 percent (to 90 V). By what percentage is the power reduced

percent decrease in power  = 20 % .

Explanation:

Power P = v² / R where v is voltage and R is resistance which is constant .

taking log on both sides

log P = 2 log v - log R

differentiating on both sides

dP/P = 2 dv/v

-dP/P x 100 = 2 x -dv/v x 100

percent decrease in power = 2 x percent decrease in v ( voltage )

percent decrease in power = 2 x 10 = 20 %

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