User:AJim/step

step response
Another way to understand the lag in current is by considering the inductor current in response to a step change in applied voltage. Step changes in applied voltage are often encountered in switching circuits. Recall equation (1), $$\; v(t) = L\,\frac{\text{d}i }{\text{d}t}.\;$$ If we rearrange terms we see that, if V is constant, $$\frac{\text{d}i }{\text{d}t} = \frac{V}{L}\;$$ Thus, a step change from zero to 1 Volt across an inductor of 1 Henry produces a current which increases, from zero, at the constant rate of 1 Amp/Second. As long as this voltage persists, this lagging current will increase, until some physical limit is reached, such as the maximum current the voltage source can supply, the current the wire can sustain without melting, or the magnetic field the inductor can support without saturating. Also, note the reciprocal relationship of L. In the same circuit, an inductor of 0.5 Henry will result in a current increasing at 2 Amp/Second.