Voltage Division in Series Resistors

Steps:

• Total resistance is R1 + R2; current I is total voltage V divided by total resistance.
• V1 = I × R1, so V1 = V × (R1 / (R1 + R2)).
• V2 = I × R2, so V2 = V × (R2 / (R1 + R2)).
• Therefore, V2 / V1 = R2 / R1.

Why A is correct:

• Ohm's law and voltage divider rule state that the potential across R2 relative to R1 is proportional to their resistance ratio, so V2 = (R2 / R1) × V1.

Why the others are wrong:

• B: Inverts the ratio, giving V1 / V2 instead.
• C: Introduces unnecessary squaring of R1, not matching the linear division formula.
• D: Squares R2 incorrectly, violating the proportional division principle.

Final answer: A