Question

The current (I) varies directly as the voltage (V) in an electric circuit. If the current is 4 amperes when the voltage is 100 volts, find the current when the voltage is 75 volts.

Answer 1

`\bf \begin{array}{cccccclllll} \textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\ \textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\ y&=&{{ k}}&\cdot&x \\ && y={{ k }}x \end{array}\\\\ -----------------------------\\\\`


`\bf \textit{l varies directly to V}\implies l=kV \\\\\\ \textit{now, we also know that } \begin{cases} l=4\\ V=100 \end{cases}\implies 4=k100 \\\\\\ \cfrac{4}{100}=k\implies \cfrac{1}{25}=k\impliedby \textit{constant of variation} \\\\\\ thus\implies l=\cfrac{1}{25}V \\\\\\ \textit{what is the current when the voltage is 75?}\qquad l=\cfrac{1}{25}\cdot 75`