Question

how are the current and resistance related when the voltage of a circuit is constant?
the current doubles when the resistance doubles because they are directly proportional.
the current doubles when the resistance doubles because they are inversely proportional.
the current is cut in half when the resistance doubles because they are directly proportional.
the current is cut in half when the resistance doubles because they are inversely proportional.

Explanation:

Step1: Recall Ohm's Law

Ohm's Law is \(V = IR\), where \(V\) is voltage, \(I\) is current, and \(R\) is resistance.

Step2: Analyze when \(V\) is constant

If \(V\) is constant (\(V = k\)), then \(I=\frac{k}{R}\). This shows an inverse - proportion relationship (\(I\propto\frac{1}{R}\)).
Let the initial resistance be \(R_1\) and current be \(I_1\), so \(V = I_1R_1\). When \(R_2 = 2R_1\), then \(I_2=\frac{V}{R_2}=\frac{I_1R_1}{2R_1}=\frac{I_1}{2}\)

Answer:

The current is cut in half when the resistance doubles because they are inversely proportional.