Question

for a constant voltage, how is the resistance related to the current?
○ resistance is inversely proportional to current, so when the resistance doubles, the current is cut in half.
○ resistance is directly proportional to current, so when the resistance doubles, the current is cut in half.
○ resistance is inversely proportional to current, so when the resistance doubles, the current doubles.
○ resistance is directly proportional to current, so when the resistance doubles, the current doubles.

Explanation:

To solve this, we use Ohm's Law, which is \( V = I \times R \) (where \( V \) is voltage, \( I \) is current, and \( R \) is resistance). When voltage \( V \) is constant, we can rearrange the formula to \( I=\frac{V}{R} \). This shows that \( I \) (current) and \( R \) (resistance) have an inverse relationship (since \( I \) is equal to a constant \( V \) divided by \( R \)). So if \( R \) doubles (e.g., from \( R \) to \( 2R \)), then \( I=\frac{V}{2R}=\frac{1}{2}\times\frac{V}{R} \), meaning the current is cut in half.

Now let's analyze each option:

• Option 1: Says resistance is inversely proportional to current, and when resistance doubles, current is cut in half. This matches our analysis from Ohm's Law.
• Option 2: Claims resistance is directly proportional to current, which is wrong because from \( I = V/R \), they are inversely related.
• Option 3: Says when resistance doubles, current doubles, but inverse proportionality means if \( R \) increases, \( I \) decreases, so this is wrong.
• Option 4: Claims direct proportionality and wrong effect on current, so incorrect.

Answer:

A. Resistance is inversely proportional to current, so when the resistance doubles, the current is cut in half.