76 lines
1.4 KiB
Markdown
76 lines
1.4 KiB
Markdown
# 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.
|
||
|
||
## Thevenin’s Theorem
|
||
States that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load.
|
||
|
||
# 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:**
|
||
|
||
|
||
|
||
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
|
||
|
||
$$
|
||
\begin{flalign}
|
||
&Z = \sqrt{R^2 + X^2} &\\\
|
||
\\
|
||
&X = X_{L} - X_{C} \\
|
||
\end{flalign}
|
||
$$ |