Question

the current i in an electrical conductor varies inversely as the resistance r of the conductor. the current is \\( \frac { 1 } { 7 } \\) ampere when the resistance is 38.416 ohms. what is the current when the resistance is 12.544 ohms?
the current is ampere.
(simplify your answer type an integer or a fraction)

Explanation:

Step1: Find the constant of variation

Since \(I\) varies inversely as \(R\), the relationship is \(I=\frac{k}{R}\). When \(I = \frac{1}{7}\) and \(R = 38.416\), we substitute into the formula: \(\frac{1}{7}=\frac{k}{38.416}\). Solving for \(k\), we get \(k=\frac{38.416}{7}\).

Step2: Calculate the current when \(R = 12.544\)

Now that \(k=\frac{38.416}{7}\), and \(R = 12.544\), we use the formula \(I=\frac{k}{R}\). Substitute \(k\) and \(R\): \(I=\frac{\frac{38.416}{7}}{12.544}\). This is equivalent to \(I=\frac{38.416}{7\times12.544}\).
Calculate \(7\times12.544 = 87.808\). Then \(I=\frac{38.416}{87.808}\). Simplify the fraction: \(\frac{38.416\div38.416}{87.808\div38.416}=\frac{1}{2.285714}\approx\frac{1}{ \frac{16}{7}}=\frac{7}{16}\) (alternatively, \(38.416\div12.544 = 3.0625\), \(3.0625\div7=\frac{3.0625}{7}=\frac{30625\div125}{70000\div125}=\frac{245}{560}=\frac{7}{16}\)).

Answer:

\(\frac{7}{16}\)