Circuit Response
every model has an edge, and the figure carries it
Generator

Superposition holds for the solution and not for its square

computed by solving, not by drawing, at 81 settings of the second source. Two ten-volt sources reach one hundred-ohm load through a hundred ohms each. Every node voltage and every branch current is the sum of the two single-source solves to 3.8e-16 of itself — superposition, exactly. The power is not: the difference is 2·Re(I₁·conj(I₂))·R to 1.0e-15, and at 0° between the sources and equal size it is 444.4 mW against the 222.2 mW that adding gives. Adding the two powers is within one per cent of the truth only when one source is below 0.00505 of the other. The slider is the angle between them: at 90° the two curves coincide to the last bit, and at 180° the true power falls to zero while the sum does not.
Superposition holds for the solution and not for its squarecomputed by solving, not by drawing, at 81 settings of the second source. Two ten-volt sources reach one hundred-ohm load through a hundred ohms each. Every node voltage and every branch current is the sum of the two single-source solves to 3.8e-16 of itself — superposition, exactly. The power is not: the difference is 2·Re(I₁·conj(I₂))·R to 1.0e-15, and at 0° between the sources and equal size it is 444.4 mW against the 222.2 mW that adding gives. Adding the two powers is within one per cent of the truth only when one source is below 0.00505 of the other. The slider is the angle between them: at 90° the two curves coincide to the last bit, and at 180° the true power falls to zero while the sum does not.020040060080000.50011.502the second source, as a multiple of the firstpower into the load (milliwatts)the two powers, addedwhat the load actually getsphase between them0°at equal size, truly444.4 mWadding the two powers222.2 mWtruth ÷ the sum2.000×within 1% only below0.00505×voltages add to3.8e-16solved, then checked — three solves, one loadpowers add only at 90°, or beyond 198:1

Drawn above at its default parameters, which is almost never how an essay calls it. A placement states the numbers that essay is arguing about, so the figure a reader meets is about that argument rather than about the generator — 98% of the placements on this site pass one, and the phase that raised that number from 12% found eight captions describing a figure the page was not showing.

At those defaults the edge it states is powers add only at 90°, or beyond 198:1 — the right-hand slot of the caption strip, which on this site is never used for anything else, and which is read back out of the drawing above rather than out of the code that wrote it. It belongs to Networks, and how a solve is checked, which is to say a change to it is a change to lib/figures/networks.js. It takes a slider on the angle between the two sources (degrees) with 7 settings, and every one of them has passed the same assertions as the frame above — a figure whose circuit stops doing what its caption says at any setting stops the build.

Called by 1 essay

which is the blast radius of changing it

Two solves that add, and the one that does not

Every node voltage and every branch current in a linear network is the sum of the per-source solves, here to the last bit of a double at eighty-one settings. The power is not, and the gap is not a correction: two equal sources in antiphase put nothing at all into a load while adding their powers gives 222 milliwatts, and the sum is within one per cent of the truth only when one source is two hundred times the other.

Networks, and how a solve is checked

Every generator