Why does current lead voltage in a capacitor and lag voltage in an inductor?

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Why does current lead voltage in a capacitor and lag voltage in an inductor?

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When you are charging a capacitor initially it’s empty, so even when the voltage is low a lot of current is going to flow in order to charge it, and so current is leading the voltage, then as the voltage drops, the capacitor still has charge, so it will put the current back

Inductors instead resist the change in current by building a magnetic field, so when the voltage is high, it’s still generating a magnetic field and can’t let all the current through, after it’s all charged up current will continue to flow as the magnetic field collapses, making the current lag behind