If the current through a resistor doubles while resistance stays the same, by what factor does the power dissipated increase?

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Multiple Choice

If the current through a resistor doubles while resistance stays the same, by what factor does the power dissipated increase?

Explanation:
Power dissipated in a resistor grows with the square of the current when the resistance is fixed. The formula P = I^2R shows this directly. If the current doubles (I → 2I) while R stays the same, the new power is P' = (2I)^2R = 4I^2R = 4P. So the power increases by a factor of four. (Equivalently, since V = IR, doubling current with the same R doubles the voltage, and P = V^2/R gives P' = (2V)^2/R = 4P.)

Power dissipated in a resistor grows with the square of the current when the resistance is fixed. The formula P = I^2R shows this directly. If the current doubles (I → 2I) while R stays the same, the new power is P' = (2I)^2R = 4I^2R = 4P. So the power increases by a factor of four. (Equivalently, since V = IR, doubling current with the same R doubles the voltage, and P = V^2/R gives P' = (2V)^2/R = 4P.)

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