Question

the current i in an electrical conductor varies inversely as the resistance r of the conductor. the current is 6 amperes when the resistance is 910 ohms. what is the current when the resistance is 510 ohms? the current is □ amperes. (round to the nearest hundredth.)

Explanation:

Step1: Write the inverse - variation formula

Since \(I\) varies inversely as \(R\), the formula is \(I=\frac{k}{R}\), where \(k\) is the constant of variation.
We know that when \(I = 6\) amperes and \(R=910\) ohms. Substitute these values into the formula: \(6=\frac{k}{910}\).

Step2: Solve for \(k\)

Multiply both sides of the equation \(6=\frac{k}{910}\) by \(910\): \(k = 6\times910=5460\).
So the equation of variation is \(I=\frac{5460}{R}\).

Step3: Find \(I\) when \(R = 510\)

Substitute \(R = 510\) into the equation \(I=\frac{5460}{R}\): \(I=\frac{5460}{510}\approx10.71\)

Answer:

\(10.71\)