Ohms Law

Solve for voltage:


\begin{flalign}
V &= \frac{I}{R}&
\end{flalign}

Solve for resistance:


\begin{flalign}
R &= \frac{V}{I} &
\end{flalign}

Solve for current


\begin{flalign}
I & = \frac{V}{R} &
\end{flalign}

Resistors in Series


\begin{flalign}
R &= R1 + R2 + R3 ... &
\end{flalign}

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:


\begin{flalign}
i1 = i2 + i3 + i4 &&
\end{flalign}

Conservation of Energy (Second Law)

All the potential differences around the loop must sum to zero.


\begin{flalign}
\sum{V} = 0 &&
\end{flalign}

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