A inductor is a device which relates flux and voltage.

If the flux-current relation is linear, as shown in Figure 1(a), then:

$$\varphi = Li\\ \label{eq:yli}$$

where the constant, $$L$$, is defined as the device inductance. The SI units of inductance are henries (H). Since $$i=g(t)$$, then differentiating both sides of equation \eqref{eq:yli} with respect to time admits the following voltage-current relation:

$$\frac{d\varphi}{dt} = v = L\frac{di}{dt} \\ \label{eq:dydt}$$

If the flux-current relation is non-linear, as shown in Figure 1(b), then:

$$\varphi = f(i) \\ \label{eq:yfi}$$

Since $$i=g(t)$$, then differentiating both sides of equation \eqref{eq:yfi} with respect to time (using the Chain rule) admits the following current-voltage relation:

$$\frac{d\varphi}{dt} = \frac{d\varphi}{di}\frac{di}{dt} \\ \label{eq:dydt1}$$ $$v = L(i)\frac{di}{dt} \\ \label{eq:dydt2}$$

The inductance, $$L(i)$$, is defined as:

$$L(i) = \frac{d\varphi}{di} \\ \label{eq:li}$$