# Inductor **A passive two-terminal electrical component that stores energy in a magnetic field when current flows through it.** ![[Inductor.svg|200]] An inductor is typically a coil of wire and is characterised by its [[inductance]]. The *current* through an inductor *can not* change *instantaneously*, as this would theoretically collapse and induce a magnetic field instantly. ## Inductors in series and parallel > [!Series] The total inductance of a *series* of inductors is the sum of the individual inductances. $L_{\text{eq}}=L_1+L_{2}+\cdots+L_{n}$ > ![[InductorsSeries.svg|600]] > [!Parallel] The total inductance of *parallel* inductors is the reciprocal of the sum of the reciprocals of their inductances. $L_{\text{eq}}=\frac{1}{\frac{1}{L_1}+\frac{1}{L_{2}}+\cdots+\frac{1}{L_{n}}}$ > ![[InductorsParallel.svg|600]] ## Impedance > [!Impedance] > The [[impedance]] of an inductor is > $\mathbf{Z}=j\omega L$ > - $\omega$ - [[angular frequency]], radians per second > - $L$ - [[inductance]], $\text{H}$ The current *lags* the voltage by $90^{\circ}$ in an inductor. At DC, an inductor acts like a *short circuit* as the lack of changing current means no opposing magnetic fields are induced. At high frequencies, an inductor acts like an *open circuit* as the rapidly changing current will be mitigated by the induction of opposing magnetic fields. ![[InductorFrequencyResponse.svg|550]] ## Voltage > [!Voltage] > The *voltage* across an inductor is > $V=L \frac{di}{dt}$ Note that this implies that the current through an inductor *can not* change *instantaneously*, as this would require an infinitely large applied voltage. ## Current > [!Current] > The *current* through an inductor is > $i(t)=\frac{1}{L}\int_{t_0}^{t}v(t)\;dt+i(t_{0})$ ## Stored energy > [!Stored energy] > The *energy* stored in the magnetic field of an inductor is > $w(t)=\frac{1}{2}L\;i(t)^2$