A rapid increase in voltage with a duration of half a cycle best describes a(n):

A swell is a sustained RMS voltage increase above nominal lasting from 0.5 cycles to several minutes, making its duration far longer than the half-cycle described.

An overvoltage is a prolonged steady-state condition where voltage remains above nominal for more than one minute, not a brief half-cycle spike.

A transient is a sudden, brief voltage disturbance lasting half a cycle or less, typically caused by switching events or lightning surges. Its defining characteristics are high amplitude and extremely short duration, which precisely matches 'rapid increase lasting half a cycle.' This short duration distinguishes it from all other power quality events, which persist for multiple cycles or longer.

A frequency variation is a deviation in the AC line frequency in hertz from its nominal value, not a change in voltage magnitude or duration.