A inductor is a device which relates flux and voltage.

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Flux-current relationship of linear and non-linear inductance.

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:

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