# ELI the ICE man

by leright
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 Sci Advisor HW Helper P: 1,326 Realizing that $$j = e^{j\frac{\pi}{2}}$$, multiplying by $$j$$ amounts to adding 90 degrees to the exponential. In elaboration of what berkeman has described: $$V = L \frac{di}{dt}=L j \omega e^{j \omega t} = L \omega e^{j( \omega t + \frac {\pi}{2})$$. The output voltage (V) is ahead (leads) the input current (I) by 90 degrees through an inductor. (Plot it and you can see). By analogous reasoning, you can show current leading voltage by 90 degrees across a capacitor.