AC Theory Cheatsheet – Bit Shift My Robot

Inductance is the relationship between the current and the magnetic field generated in a coil. Each is proportional to the delta of the other.

$L = \frac{d^2 n^2}{l + 0.45d}$
$d$ is diameter of coil in meters, $n$ is number of coil turns, $l$ is length of coil in meters
Resistance (R) is not affected by AC voltage or current frequency and remains the same for AC/DC

$R = \frac{V}{I}$
Reactance (X) or Back EMF is the opposition to current flow in proportion to the current frequency
- Inductive reactance ( $X_L$ ) rises with an increase in frequency:
  
  $X_L = 2 \pi f L$
- Capacitive reactance ( $X_C$ ) rises with a decrease in frequency:
  
  $X_C = \frac{1}{2 \pi f C}$
Impedance describes the combined effect of resistance (R), inductive reactance ( $X_L$ ) and capacitive reactance ( $X_C$ ) in an AC circuit. For DC circuit:

$Z = \sqrt{R^2 + X_C^2}$
For AC circuit:

$Z = \sqrt{R^2 + (X_L - X_C)^2}$