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[1] Leading and lagging current are phenomena occuring due to alternating current. A circuit with AC's voltage and current value and vary sinusoidally.
In such circuits, the term "lead", "lag", and "in phase" depict current by reference to voltage.
[1] Current is in phase to voltage without phase shift between the sinusoids depicting their time varying behavior. This often occurs if the load drawing the current is resistive.
Current is leading if its peaks, zero-crossings, and overall cycle occur earlier in time than the reference wave of the same frequency. This time difference is known as a phase lead.
Current is lagging if its peaks, zero-crossings, and overall cycle occur later in time than the reference wave of the same frequency. This time difference is known as a phase lag.
[1] Wikipedia