Question

which statement describes the relationship of resistance and current?

resistance is directly proportional to current because ( r = \frac{v}{i} ).

resistance is inversely proportional to current because ( r = \frac{v}{i} ).

resistance is directly proportional to current because ( r = vi ).

resistance is inversely proportional to current because ( r = vi ).

Explanation:

1. Recall Ohm's Law: The correct formula for resistance is \( R=\frac{V}{I} \) (where \( V \) is voltage, \( I \) is current, and \( R \) is resistance).
2. Analyze proportionality: For a fixed voltage (\( V \) constant), if current (\( I \)) increases, resistance (\( R \)) decreases, and vice versa. This means \( R \) is inversely proportional to \( I \) when \( V \) is constant.
3. Evaluate options:

• The first option is wrong because \( R \) is not directly proportional to \( I \) (from \( R = \frac{V}{I}\), with \( V \) constant, \( R\propto\frac{1}{I}\)).
• The second option is correct: \( R=\frac{V}{I} \), and with \( V \) constant, \( R \) and \( I \) are inversely proportional.
• The third and fourth options use the wrong formula (\( R = VI \) is incorrect; the correct formula is \( R=\frac{V}{I} \) or \( V = IR \)), so they are eliminated.

Answer:

B. Resistance is inversely proportional to current because \( R=\frac{V}{I} \) (assuming the second option is labeled as B; adjust label based on original question's option numbering, but the content is "Resistance is inversely proportional to current because \( R = \frac{V}{I} \)").