# Inductance **The tendency of an electrical conductor to oppose a change in the current flowing through it.** > [!infobox] Inductance > | | | |:---------------- | ----------------------------------------------:| | ***Symbol*** | $L$ | | ***SI unit*** | henry, $\text{H}$ | | ***SI base units*** | $\text{kg}\;\text{m}^2\;\text{s}^{-2}\;A^{-2}$ | *Inductance* is defined as the ratio of the *induced voltage* to the *rate of change* of the *current* causing it. An electrical conductor will *induce* a magnetic field around it when a *changing* electric current is flowing through it, as described in [[Faraday's law of induction]]. This magnetic field in turn induces a *back EMF* that opposes the change in current according to [[Lenz's Law]]. Inductance depends on the *geometry* of the conductor and the *magnetic permeability* of nearby materials, such as the core. A component designed specifically to add inductance is known as an [[inductor]] which usually consists of a coil of wire. The voltage an inductor induces across itself is caused by its *self inductance*. ## Mutual inductance *Mutual inductance* is the phenomenon in which the magnetic flux caused by the current through an inductor induces a voltage in another in proximity. Mutual inductance is also the measurement of the amount of *magnetic coupling* between the inductors. Suppose there are two coils, coil 1 and coil 2: ![[MutualInductance.svg]] The *total flux*, $\phi$, of coil 1 is equal to $\phi_{11}+\phi_{12}$. The effect of $\phi_{11}$, where the subscript denotes the effect of coil 1 on coil 1, is the effect of the *self inductance* of the coil. It can be expressed as follows: $v_{1}=L_{1}\frac{di_{1}}{dt}\Longleftrightarrow\mathbf{v}_{1}=j\omega L_{1}\mathbf{I}_{1}$ The effect of $\phi_{12}$ is the effect of the *mutual inductance* between the coils, denoted as $M$ and also measured in *henrys*, $H$. $v_{2}=M\frac{di_{2}}{dt}\Longleftrightarrow\mathbf{v}_{2}=j\omega M\mathbf{I}_{2}$ This is also true in reverse, as in, if coil 2 was connected to the current source instead of coil 1. Note the *polarity* of the voltages are *not* explicitly stated in the above equations and the symbols on the diagram are arbitrary definitions. The polarity of the voltages and direction of current requires [[dot convention]] to specify.