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:

To solve this, we use Ohm's Law, \( I=\frac{V}{R} \) (where \( I \) is current, \( V \) is voltage, \( R \) is resistance). When \( V \) is constant, \( I \propto \frac{1}{R} \) (inversely proportional). If \( R \) doubles (\( R_2 = 2R_1 \)), then \( I_2=\frac{V}{2R_1}=\frac{1}{2}\times\frac{V}{R_1}=\frac{I_1}{2} \). So current is halved when resistance doubles, and they are inversely proportional.

Answer:

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