Inductors#
\[\Phi(t) = L i(t)\]
\[i(t) = \frac{1}{L} \Phi(t)\]
Theorem: Energy
The total change in the energy of an inductor whose flux linkage changes from \(\Phi_{\text{initial}}\) to \(\Phi_{\text{final}}\) is given as follows:
\[\frac{1}{2L}(\Phi_{\text{final}}^2 - \Phi_{\text{initial}}^2)\]
The total change in the energy of an inductor whose current changes from \(I_{\text{initial}}\) to \(I_{\text{final}}\) is given as follows:
\[\frac{1}{2}L(I_{\text{final}}^2 - I_{\text{initial}}^2)\]
Proof
TODO