notes/Areas/electricity/formulas.md

1.2 KiB

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:

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}