Question

the current i in an electrical conductor varies inversely as the resistance r of the conductor. the current is 1/2 ampere when the resistance is 224 ohms. what is the current when the resistance is 2.744 ohms? the current is □ ampere. (simplify your answer. type an integer or a fraction)

Explanation:

Step1: Find the relationship formula

Since the current \(I\) varies inversely as the resistance \(R\), the relationship is \(I=\frac{k}{R}\) (where \(k\) is a constant).
When \(I = \frac{1}{2}\) ampere and \(R = 224\) ohms, we substitute into the formula \(\frac{1}{2}=\frac{k}{224}\).

Step2: Solve for \(k\)

Cross - multiply: \(k=\frac{1}{2}\times224 = 112\). So the formula is \(I=\frac{112}{R}\).

Step3: Calculate the current when \(R = 2.744\) ohms

Substitute \(R = 2.744\) into \(I=\frac{112}{R}\), then \(I=\frac{112}{2.744}=\frac{112\times1000}{2744}=\frac{112000}{2744}=\frac{112000\div 8}{2744\div 8}=\frac{14000}{343}=\frac{14000\div 7}{343\div 7}=\frac{2000}{49}\)

Answer:

\(\frac{2000}{49}\)