Inductance Notes

When current flows through one circuit, the magnetic field it produces can create a flux through a nearby circuit, inducing an EMF in the second circuit.
The effectiveness of one circuit inducing an EMF in another is called mutual inductance.
Mutual inductance depends on geometrical factors (proximity, area, number of turns, shape) and is analogous to capacitance.
$M{21} = \frac{N2 \phi{21}}{I1}$ , where:
- $M_{21}$ is the mutual inductance of coil 2 due to coil 1.
- $N_2$ is the number of turns in coil 2.
- $\phi_{21}$ is the flux created by coil 1 going through coil 2.
- $I_1$ is the current in coil 1.
Flux linkage is the total flux through all turns of a coil ( $N2 \phi{21}$ ).
$M{12} = \frac{N1 \phi{12}}{I2}$ is the mutual inductance of coil 1 due to coil 2.
The mutual inductance of coil 2 due to coil 1 is the same as that of coil 1 due to coil 2 ( $M{21} = M{12} = M$ ).
Units for inductance are Henrys (H), where 1 Henry = volt-seconds per amp.
Mutual inductance is the basis of transformers and induction cooktops.

A circuit will induce an EMF in itself because the current in the wire creates a magnetic field and flux through its own loop.
Self-inductance is the ability of a circuit to induce an EMF within itself.
The induced EMF opposes the change in current.
$L = \frac{N\phi}{I}$ , where:
- $L$ is the self-inductance.
- $N$ is the number of turns.
- $\phi$ is the magnetic flux.
- $I$ is the current.
Total EMF in a circuit is the sum of self-induced EMF and mutually induced EMF from other circuits.
$EMF{total} = EMF{self} + EMF_{mutual}$
$EMF{self} = -L \frac{dI1}{dt}$
$EMF{mutual} = -M \frac{dI2}{dt}$
Self-inductance (L) is always positive, while mutual inductance (M) can be positive or negative based on circuit arrangement.
Self-inductance can be a nuisance (causing sparks) but also has useful applications, such as security detectors and traffic lights.