If you double the resistance while holding the voltage constant, what happens to the power dissipated?

If you double the resistance while holding the voltage constant, what happens to the power dissipated?

• A. Power doubles
• B. Power stays the same
• C. Power decreases slightly
• D. Power halves

Answer: (D)

Power dissipated by a resistor with a fixed voltage is inversely proportional to resistance. When voltage stays the same and you double the resistance, the current drops because I = V/R. Doubling R makes I half as large, and since power is P = V × I, halving the current with the same voltage gives P = V × (V/2R) = (1/2) × (V^2/R). So the power becomes half of what it was before. An equivalent way to see it is P = V^2 / R; increasing R to 2R makes P drop to V^2/(2R), which is half of V^2/R.

Power dissipated by a resistor with a fixed voltage is inversely proportional to resistance. When voltage stays the same and you double the resistance, the current drops because I = V/R. Doubling R makes I half as large, and since power is P = V × I, halving the current with the same voltage gives P = V × (V/2R) = (1/2) × (V^2/R). So the power becomes half of what it was before. An equivalent way to see it is P = V^2 / R; increasing R to 2R makes P drop to V^2/(2R), which is half of V^2/R.