Mathematics, 30.06.2019 01:10 lpierce35
In physics, ohm's law says that current through a wire, i, is directly proportional to voltage, v, and inversely proportional to resistance, r:
i=v/r.
it's also true that resistance is directly proportional to the length of the wire. we have a piece of wire. we pass 12 volts through this wire and measure 100 milliamps of current. if i cut the wire in half and pass 24 volts through it, how many milliamps of current will i measure?
Answers: 2
![\bf \qquad \qquad \textit{compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill](/tpl/images/0033/0394/0a75c.png)
![\bf \stackrel{\textit{I varies directly with V and inversely with R}}{I=\cfrac{(1)V}{R} }~\hfill \leftarrow k=1\to ~\hfill \stackrel{\textit{R varies directly with L}}{R=(1)L} \\\\[-0.35em] ~\dotfill\\\\ \textit{we know that } \begin{cases} V=12\\ I=100 \end{cases}\implies 100=\cfrac{(1)12}{R}\implies R=\cfrac{12}{100}\implies R=\cfrac{3}{25}](/tpl/images/0033/0394/4484d.png)
![\bf I=\cfrac{V}{R}\implies I=\cfrac{\stackrel{V}{24}}{\stackrel{\textit{halved R}}{\frac{3}{25}\div 2}}\implies I=\cfrac{24}{\frac{3}{25}\cdot \frac{1}{2}}\implies I=\cfrac{24}{\frac{3}{50}} \\\\\\ I=\cfrac{\stackrel{8}{~~\begin{matrix} 24 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{1}\cdot \cfrac{50}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies I=400](/tpl/images/0033/0394/3cd68.png)
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