The voltage across an inductance l is given by v(t)=vmcos(ωt). the current is zero at t = 0. suppose that ω is very large ideally, approaching infinity. part a for this voltage, does the inductance approximate either an open or a short circuit? for this voltage, does the inductance approximate either an open or a short circuit? i(t)=1l∫t0v(t)dt+i(0)=1l∫t0vmcos(ωt )dt=vmωlsin(ωt). for ω→[infinity], the current becomes zero, so the inductance becomes the equivalent of an open circuit. i(t)=1l∫t0v(t)dt+i(0)=1l∫t0vmcos(ωt )dt=ωvmlsin(ωt). for ω→[infinity], the current becomes infinite, so the inductance becomes the equivalent of a short circuit.