Question

which statement describes the relationship of voltage and current?
voltage is directly proportional to current because ( i = \frac{v}{r} ).
voltage is inversely proportional to current because ( i = \frac{v}{r} ).
voltage is directly proportional to current because ( i = vr ).
voltage is inversely proportional to current because ( i = vr ).

Explanation:

To determine the relationship between voltage (\( V \)) and current (\( I \)), we use Ohm's Law, which is \( I=\frac{V}{R} \) (where \( R \) is resistance, assumed constant for this relationship analysis). In a direct proportionality, if one quantity increases, the other increases proportionally when a third quantity (here, \( R \)) is constant. From \( I = \frac{V}{R} \), we can rearrange it as \( V=IR \). When \( R \) is constant, as \( V \) increases, \( I \) increases (since \( I=\frac{V}{R} \), if \( V \) goes up and \( R \) stays the same, \( I \) must go up). Let's analyze each option:

• Option 1: "Voltage is directly proportional to current because \( I = \frac{V}{R} \)". From \( I=\frac{V}{R} \), we can think of \( V = IR \). If \( R \) is constant, when \( V \) increases, \( I \) increases (since \( I=\frac{V}{R} \), so \( V \) and \( I \) have a direct relationship when \( R \) is constant). This is correct.
• Option 2: Says voltage is inversely proportional to current, but from \( I=\frac{V}{R} \), when \( R \) is constant, \( V \) and \( I \) are directly proportional, not inverse. So this is wrong.
• Option 3: The formula \( I = VR \) is incorrect. Ohm's Law is \( I=\frac{V}{R} \), not \( I = VR \). So this is wrong.
• Option 4: The formula \( I = VR \) is incorrect, and also the inverse proportionality claim is wrong.

Answer:

A. Voltage is directly proportional to current because \( I = \frac{V}{R} \)