Inductors

• Stores energy in a Magnetic Fields
• $N\varphi =Li$
  • where N is the number of turns in the inductor
  • $\varphi$ is the magnetic flux
  • L is the inductance in Henrys (H)
• Law of electromagnetic induction says that $\frac{\mathrm{d}(N\varphi )}{\mathrm{d}t}=\frac{\mathrm{d}(Li)}{\mathrm{d}t}=V=L\frac{\mathrm{d}i}{\mathrm{d}t}$
  • When current is constant, inductor is a short circuit
• Energy stored: $w(t)=\frac{1}{2}L{i}^2$
• because of the derivative, $\mathbf{V}$ leads $\mathbf{I}$ by $90\text{°}$ and $\mathbf{V}=j\omega L\mathbf{I}$
  • ELI
• $Z_L=j\omega L$

Equivalent Inductors

• Behaves like resistors
• In series, the inductances add
• in parallel, $\frac{1}{L_{eq}}=\frac{1}{L_1}+\frac{1}{L_2}+\dots$