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Resistor Power: What Stays Equal?

Compare power using equal current in series and equal voltage in parallel.

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Use steady ideal resistors and an ideal fixed source. Series resistors share a current: P = I x I x R, so the larger resistance dissipates more power within that pair. Complete parallel branches share a voltage: P = V x V / R, so the smaller resistance dissipates more power. The condition held equal matters. Use paper models only, not a physical build.

Worked example

At a shared series current of 0.02 A, a 100-ohm resistor dissipates 0.02 x 0.02 x 100 = 0.04 W and 200 ohms dissipates 0.08 W. At a shared parallel voltage of 6 V, their powers are 36 / 100 = 0.36 W and 36 / 200 = 0.18 W. Changing the layout changes what is equal.

Series comparison: both resistors carry 0.02 amp, with 100 ohms at 0.04 watt and 200 ohms at 0.08 watt. Parallel comparison: both have 6 volts, with 100 ohms at 0.36 watt and 200 ohms at 0.18 watt.
Compare the stated equal quantity before predicting which resistor has more power.
Question 1 In a series pair carrying 0.04 A, what is the power of its 100-ohm resistor?
Question 2 The same series pair also has a 200-ohm resistor. What is its power?
Question 3 A separate 100-ohm resistor is connected across an ideal 12 V source. What is its power?
Question 4 Another parallel branch has 200 ohms across the same 12 V. Which branch has more power?
Question 5 Does a larger resistance always mean less power?