Question

The current I  in an electrical conductor is inversely proportional to its resistance R . If the current is 1 /4  ampere when the resistance is 100  ohms, what is the current when the resistance is 150  ohms? Keep your answer in rational form and omit units.

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \textit{I is inversely proportional to R}\implies I = \cfrac{k}{R} \\\\\\ \textit{we also know that } \begin{cases} I=\stackrel{Amps}{\frac{1}{4}}\\ R=\stackrel{Ohms}{100} \end{cases}\implies \cfrac{1}{4}=\cfrac{k}{100}\implies \cfrac{100}{4}=k \\\\\\ 25=k\qquad \qquad \boxed{I=\cfrac{25}{R}} \\\\\\ \textit{when R = 150, what is \underline{I}?}\qquad \qquad I=\cfrac{25}{150}$