77 lines
1.1 KiB
Markdown
77 lines
1.1 KiB
Markdown
# Ohms Law
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Solve for voltage:
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$$
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\begin{flalign}
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V &= \frac{I}{R}&
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\end{flalign}
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$$
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*Solve for resistance:*
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$$
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\begin{flalign}
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R &= \frac{V}{I} &
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\end{flalign}
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$$
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_Solve for current_
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$$
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\begin{flalign}
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I & = \frac{V}{R} &
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\end{flalign}
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$$
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# Resistors in Series
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$$
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\begin{flalign}
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R &= R1 + R2 + R3 ... &
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\end{flalign}
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$$
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# Resistors in Parallel
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$$
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\begin{flalign}
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\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} ... &&\\
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\\
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\textit{For two resistors in parallel:} &&\\
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\\
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R = \frac{R1 * R2}{R1 + R2} &&\\
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\end{flalign}
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$$
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***Tip:***
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If resistors of the same value are in parallel the total resistance is a single resistor divided by the amount if resistors.
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# Kirchhoff's Law
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## Conservation of Charge (First Law)
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All current entering a node must also leave that node
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$$
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\begin{flalign}
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\sum{I_{IN}} = \sum{I_{OUT}}&&
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\end{flalign}
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$$
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**Example:**
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For this circuit kirchhoffs law states that:
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$$
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\begin{flalign}
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i1 = i2 + i3 + i4 &&
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\end{flalign}
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$$
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## Conservation of Energy (Second Law)
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All the potential differences around the loop must sum to zero.
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$$
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\begin{flalign}
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\sum{V} = 0 &&
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\end{flalign}
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$$
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