Inductor / Inductance

An inductor consists of a conducting wire in the form of a coil. It stores energy in its magnetic field.

Resources:

• Induction - An Introduction: Crash Course Physics #34
• How Inductors Work by Engineering Mindset
• Inductors Explained - The basics how inductors work working principle by Engineering Mindset

Inductance relates how a changing current in a conductor creates a magnetic field.

ECE140

• Inductors are used extensively in analog circuits and signal processing, but I have no idea for what $v(t)=L\frac{di(t)}{dt}$ where $L$ is inductance, a constant measured in Henry (H), $1H=1\frac{V.s}{A}$

Values of inductor depend on:

• Physical dimensions of inductor
• number of coil turns
• Material of core

Some Remarks

Similar to the Capacitor for voltage, the current cannot jump suddenly for an Inductor.

$i(t)=\frac{1}{L}{\int }_{t_0}^{t}v(\tau )d\tau +i(t_0)$

Power $p(t)=v(t)i(t)=Li(t)\frac{di(t)}{dt}$ Energy $w(t)=\frac{1}{2}L{i}^2(t)$

title: Inductor and DC Current (Short Circuit)
If the current $i(t)$ is constant (DC current), then the inductor acts like an **short circuit**.

Combinations of Inductors

Inductors can be combined to form parallel inductors and series inductors.

For series inductors, the formula is $L_{eq}=L_1+L_2+L_3+\dots$

For parallel inductors, the formula is $\frac{1}{L_{eq}}=\frac{1}{L_1}+\frac{1}{L_2}+\frac{1}{L_3}+\dots$

Inductor for AC

ECE106

When the question asks for inductance, use this formula $L=\frac{\Lambda }{I}$ where $\Lambda =N{\Phi }_m$

Induced voltage stuff $V_{ind}=NL\frac{d\Phi }{dt}$

Inductance per unit length is given by (just divide the inductance by length $l$): $\frac{L}{l}$

Self-inductance vs. Mutual Inductance

To clarify, Brenda didn’t explaint his well Self-inductance → Find inductance of object itself. Self-inductance is the ratio of the magnetic flux through the inductor to the current in the inductor.

$V_{ind}=-L\frac{di}{dt}$ where $L=\frac{\Lambda }{I}$ Mutual inductance → Find inductance of object 1 on object 2 Changing current in a coil induces $V_{ind}$ in another coil.

We represent the mutual inductance by the symbol $M$.

$M=\frac{{\Lambda }_{12}}{I_1}$

Magnetic Energy Density

Related

• Conductor