### Mutual Induction

Variant of Faraday’s Law

$ϵ_{2}=−MdtdI_{1} $**ϵ** = EMF (V)
M = Mutual Inductance (H, Henrys)
I = Current (A)

- This is how wireless charging works! The magnetic field can transfer power!
- Two coils interacting with each other

$ϵ_{1}ϵ_{2} =N_{1}N_{2} $

**ϵ** = EMF (V)
N = Number of Turns

- The ratio in between the two EMF’s is the same as the ratio in between the amount of turns of looped wire!
- These are how
**transformers work**. You can step higher voltage down to lower voltage. Power brick transformers step 120V down to 12V for our devices! - Going from low voltage to high voltage works this way, (12V-120V), but there will always be a trade off.
- (eg, more loops equals more resistance, (V=IR), so your voltage may be higher, but the current will drop)

##### Transformers!

### Self Inductance

$ϵ=−LdtdI $**ϵ** = EMF (V)
L= Self Inductance (H, Henrys)
I = Current (A)

- L, the curly thing in the circuit, is an
**INDUCTOR**

Current change over time due to this EMF

#### Closing the Switch (Current growing to max)

Current at a time:

$I(t)=I_{max}(1−e_{−τ1})$Time Constant:

$τ=RL $Half Time:

$t_{21}=0.69τ$#### Opening the Switch (Current going from max to 0A)

Current at a time:

$I(t)=I_{max}e_{−τ1}$Time Constant:

$τ=RL $- This is cool, because this is how surge protectors work!
- The exponential growth slows surging current, and a high inductance can slow surges.
- The slope is nicer to electronics

#### Inductors can store and release energy!

- This can be defined by the following equation

U = Energy stored/released L = Self Inductance (H, Henrys) I = Current (A)