Question

in an electrical circuit, the current passing through a conductor varies inversely with the resistance. suppose that when the current is 14 a (amperes), the resistance is 10 ohms. what is the resistance when the current is 5 a?

Explanation:

Step1: Write the inverse - variation formula

Since current \(I\) varies inversely with resistance \(R\), the formula is \(I=\frac{k}{R}\), where \(k\) is the constant of variation.
When \(I = 14\) A and \(R=10\) ohms, we substitute into the formula: \(14=\frac{k}{10}\).

Step2: Solve for \(k\)

Multiply both sides of the equation \(14=\frac{k}{10}\) by \(10\): \(k = 14\times10=140\).

Step3: Find \(R\) when \(I = 5\) A

Substitute \(k = 140\) and \(I = 5\) into \(I=\frac{k}{R}\), we get \(5=\frac{140}{R}\).
Cross - multiply: \(5R=140\).
Divide both sides by \(5\): \(R=\frac{140}{5}=28\).

Answer:

\(28\)