Question

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

Explanation:

To solve this, we use Ohm's Law, \( V = IR \) (where \( V \) is voltage, \( I \) is current, and \( R \) is resistance). When \( R \) is constant, we can rewrite the formula as \( I=\frac{V}{R} \). This shows that \( I \) is directly proportional to \( V \) (since \( R \) is a constant factor). So if \( V \) doubles (e.g., from \( V_1 \) to \( 2V_1 \)), and \( R \) stays the same, then \( I_1=\frac{V_1}{R} \) and \( I_2 = \frac{2V_1}{R}=2\times\frac{V_1}{R} = 2I_1 \). So the current doubles when voltage doubles because they are directly proportional.

Answer:

The current doubles when the voltage doubles because they are directly proportional.