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We can easily prove this with KVL, a little bit calculus, and trigonometry.

We get voltage as a sine function and current as a cosine function. Then we apply 'Add sugar to coffee' and get that current lags behind voltage by 90°.

But why don't we say that it leads by 270°?

Is this just convention or is there any intuitive explanation for this? Would our equations stop working if we suppose it led by 270°?

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  • $\begingroup$ Smaller numbers are just easier to work with $\endgroup$
    – naturallyInconsistent
    Commented Apr 24 at 5:59
  • $\begingroup$ $270^{\circ}=-90^{\circ} \mod 360^{\circ}$. $\endgroup$
    – Qmechanic ♦
    Commented Apr 24 at 6:05

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Because in a periodic sine function a phase of +90° is identical to a phase of -270°. You usually take the smallest value.

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