• Nikola Tesla AC Power pixel-art physics sticker, 3" × 3" / White

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Nikola Tesla Sticker

AC Slays DC Pixel Art | Physics

\[V(t) = V_0\sin(\omega t)\]
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The power in your walls alternates direction many times a second, and Tesla is part of why. AC won out for long-distance power because transformers make high-voltage transmission efficient; Tesla’s polyphase motor patents, bought by Westinghouse in 1888, made AC useful at the far end. A pixel-art portrait on a 3" × 3" sticker; the physics panel below has the equation, every symbol and the sources.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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The physics

Power lost in a wire is the current squared times the resistance, so sending power at high voltage and low current wastes much less. Transformers, which only work with alternating current, step the voltage up or down in proportion to the number of turns on each coil.

The sticker says AC Slays DC. The physics is more interesting than a fight.

Power lost in a wire is the current squared times the wire's resistance, the third formula on this page. For a fixed amount of power delivered, voltage and current trade against each other. Raise the voltage tenfold and the current falls tenfold, and the heat wasted in the line falls a hundredfold. In the 1880s the only practical way to change voltage was the transformer, developed by Lucien Gaulard and John Gibbs and made practical by William Stanley for Westinghouse in 1886; it is the second formula: two coils on an iron core, the voltage ratio set by the ratio of turns. A transformer works by induction, which happens only while current changes. It works with alternating current and does nothing for steady direct current.

Tesla's contribution was making AC useful at the far end. His polyphase system feeds a motor several alternating currents out of step with one another, so the magnetic field inside rotates by itself and drags the rotor round, with no brushes or commutator to wear out. His US patent 381,968, for an electro-magnetic motor, was issued in 1888. That May, George Westinghouse bought the rights to Tesla's polyphase patents, and it was the Westinghouse company, not Tesla alone, that fought Edison's direct-current interests for the market. Polyphase AC, in its three-phase form, still runs the grid.

The story has an epilogue. Some very long transmission links today use high-voltage direct current after all, converted at each end by power electronics that did not exist in 1888. DC was never wrong about the wire. It was missing the transformer.

The SI unit of magnetic flux density is named the tesla.

AC slays DC, then, over the distances and with the hardware of 1888.

Equations

\[V(t) = V_0\sin(\omega t)\]
\[\frac{V_s}{V_p} = \frac{N_s}{N_p}\]
\[P_{\text{loss}} = I^{2}R\]
Symbols
SymbolMeaningUnit
\(V\) voltage \(\mathrm{V}\)
\(V_0\) peak voltage \(\mathrm{V}\)
\(\omega\) angular frequency \(\mathrm{rad/s}\)
\(V_s, V_p\) secondary, primary voltage \(\mathrm{V}\)
\(N_s, N_p\) turns on secondary, primary \(\mathrm{1}\)
\(P_{\text{loss}}\) resistive power loss \(\mathrm{W}\)
\(I\) current \(\mathrm{A}\)
\(R\) line resistance \(\mathrm{Ω}\)

Source Tesla, N. (1888). A New System of Alternate Current Motors and Transformers. Transactions of the American Institute of Electrical Engineers V, 308–327.doi.org/10.1109/t-aiee.1888.5570379 (opens in a new tab)