# Ohms Law
Solve for voltage:

$\displaystyle V = \frac{I}{R}$

*Solve for resistance:*

$R = \frac{V}{I}$

_Solve for current_
$$
\begin{flalign}
I & = \frac{V}{R} &
\end{flalign}
$$

# Resistors in Series

$R = R1 + R2 + R3 ...$

# Resistors in Parallel

$$
\begin{flalign}
&\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} ... &\\
\\
&\textit{For two resistors in parallel:} &\\
\\
&R = \frac{R1 * R2}{R1 + R2} &\\\
\end{flalign}
$$

***Tip:***
If resistors of the same value are in parallel the total resistance is a single resistor divided by the amount if resistors.

# Kirchhoff's Law

## Conservation of Charge (First Law)

All current entering a node must also leave that node

$$
\begin{flalign}
\sum{I_{IN}} = \sum{I_{OUT}}&&
\end{flalign}
$$

**Example:**

![](./assets/kirchhoffs-law-01.svg)

For this circuit kirchhoffs law states that:

$\displaystyle i1 = i2 + i3 + i4$

## Conservation of Energy (Second Law)
All the potential differences around the loop must sum to zero.

$\displaystyle \sum{V} = 0$

## Capacitors in Series

$\displaystyle \frac{1}{C_{t}} = \frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} ...$

### Impedance in a Circuit

$$
\begin{flalign}
&Z = \sqrt{R^2 + X^2} &\\\
&X = X_{L} - X_{C} \\ 
\end{flalign}
$$