Inductors


What is an inductor? Wikipedia, or HowStuffWorks

The following equation represents the voltage across the terminals of an inductor as a function of the current of the inductor:
v = L
di
dt

The previous equations can be used to derive an equation which expresses the current as a function of the voltage.
Both sides of the equation are multiplied by the differential time dt. The rate at which i varies with t multiplied by a differential change in time equals a differential change in i (the two differential changes in time on the right side cancel each other out):

v dt = L di

Both sides of the equation are integrated. Choosing x and τ as the variables of integration respectively, i and t become limits on the integrals.

t
 
t0
v dτ = L
i(t)
 
i(t0)
dx

i(t) becomes the current corresponding to t and i(t0) becomes the value of the inductor current when inegration is initiated at t0
i(t) =
1
L
t
 
t0
v dτ + i(t0)

Typically the value of t0 is zero,
i(t) =
1
L
t
 
0
v dτ + i(0)