Resistor Power: Name the Equal Quantity

Explain why the power comparison depends on the circuit condition.

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For steady ideal resistors carrying the same series current, P = I x I x R. Within that pair, larger resistance dissipates more power. Across equal-voltage parallel branches, P = V x V / R, so smaller resistance dissipates more power. Do not treat either statement as a rule for every circuit. These are paper comparisons, not physical builds.

Worked example

At equal current 0.01 A, 100 ohms dissipates 0.01 W and 200 ohms dissipates 0.02 W. In a separate equal-voltage model at 2 V, 100 ohms dissipates 0.04 W and 200 ohms dissipates 0.02 W. The comparison reverses because the equal quantity changed.

Two labeled worked comparisons. Equal current 0.01 A: 100 ohms gives 0.01 W, 200 ohms gives 0.02 W. Equal voltage 2 V: 100 ohms gives 0.04 W, 200 ohms gives 0.02 W. — Name what is held equal before comparing power. These models do not predict temperatures.

Would you believe it?

A larger ideal resistor can dissipate more power at equal current, but less power at equal voltage. State what is held equal before comparing.

OpenStax: resistor power comparisons

Question 1 A series pair carries 0.03 A. What power does its 200-ohm resistor dissipate? 0.18 W 6 W 0.06 W

Question 2 The same series pair also has a 400-ohm resistor. What is its power? 0.09 W 0.36 W 0.18 W

Question 3 In a separate model, a 200-ohm resistor is across an ideal 10 V source. What is its power? 0.05 W 5 W 0.5 W

Question 4 Another parallel branch has 400 ohms across the same 10 V. Which branch has more power? The 400-ohm branch They have equal power The 200-ohm branch

Question 5 Can you say that larger resistance always gives less power without stating any other condition? No; you must specify what is held equal Yes; larger resistance always means less power Yes; larger resistance always means more power

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