# 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.

![](Inductor_diagram.svg "Inductor_diagram.svg")

### 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 $\Phi_B$) to current:

$L = \Phi_B/i$

$\Phi_B$ 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:

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

### 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
$i(t) = 5t*e^{-1000t}$ amps, what is the voltage?

Solution: No need to know the initial conditions because the solution is
a derivative: $v(t) = L di/dt$.

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

