# Circuit Theory/Inductors

An inductor is a coil of wire that stores energy in the form of a magnetic field. The magnetic field depends on current flowing to "store energy."

If the current stops, the magnetic field collapses and creates a spark in the device that is opening the circuit. The large generators found in electricity generation can create huge currents. Turning them off can be dangerous MIT EMF Youtube video. There are no dangers storing them.

## Contents

### Inductance

Inductance is the capacity of an inductor to store energy in the form of a magnetic field. Inductance is measured by units called "Henries" which is abbreviated with a capital "H," and the variable associated with inductance is "L".

Inductance is the ratio of magnetic flux (symbol ${\displaystyle \Phi _{B}}$) to current:

${\displaystyle L=\Phi _{B}/i}$

${\displaystyle \Phi _{B}}$ measures the strength of a magnetic field just like charge measures the strength of an electric field.

### Inductor Terminal Relation

The relationship between inductance, current, and voltage through an inductor is given by the formula:

${\displaystyle v=L{\frac {di}{dt}}}$

### Inductor Safety

Inductors found in power plants can store energy, but inductors found at room temperature will not store energy. An isolated inductor in storage can not kill someone like a capacitor can.

Inductors do cause problems. The first is economic. A good inductor is much more expensive than a capacitor. In some situations, a collection of other components can replace an inductor at less cost. Typical inductors are built with copper which increases in cost as supply on earth dwindles.

Inductors can create spikes and sparks video when turning off that can destroy other electrical components. They can destroy switches. They can vaporize metal.

The biggest inductors at room temperature are found in electric motors. When motors are turned on or off they create what is called a "back EMF." Ideally Back EMF is a voltage spike of infinite voltage. Diodes, capacitors and resistors are used to turn the back EMF into heat on discharge may make starting up the motor a problem. Some electronic speed controlers (ESCs) in UAVs and quadcopters pulse the motor to deliberately and measure the back EMF to figure out what direction the motor is going to spin in. This reduces the need of hall-effect probes and thus reduces the cost of the motor.

### Inductor Example

Question: Given the current through a 10mH inductor is ${\displaystyle i(t)=5t*e^{-1000t}}$ amps, what is the voltage?

Solution: No need to know the initial conditions because the solution is a derivative: ${\displaystyle v(t)=Ldi/dt}$.

Using Wolfram Alpha, the solution is ${\displaystyle v(t)=.01*e^{-1000t}(5-5000t)}$ volts.