Voltage division in series-parallel resistor network

Steps:

• The two resistors in parallel have equivalent resistance R/2 (assuming each is R).
• This R/2 is in series with the other two resistors (2R), giving total equivalent resistance 2.5R.
• Total current I = 30V / 2.5R = 12/R.
• Voltage across the series pair (between X and Y) = I × 2R = (12/R) × 2R = 24V.

Why D is correct:

• Kirchhoff's voltage law: the potential drop across the 2R section is 24V, as it carries the full current while the parallel section drops only 6V.

Why the others are wrong:

• A: Ignores the parallel combination, treating all as series (would give 22.5V across three resistors).
• B: Assumes equal voltage split across two equal sections (15V each), overlooking the parallel reduction.
• C: Mistakenly calculates voltage across a single resistor in a different configuration (e.g., total 3R equivalent).

Final answer: D