Voltage division across series resistors

Steps:

• Let resistance of X be $R$; then Y is $4R$.
• Total resistance: $R + 4R = 5R$.
• With 10 V source, current $I = 10 / 5R = 2/R$.
• $V_X = I \cdot R = 2$ V; $V_Y = I \cdot 4R = 8$ V.
• Difference: $V_X - V_Y = 2 - 8 = -6$ V (magnitude 6 V).

Why C is correct:

• Kirchhoff's voltage law gives $|V_X - V_Y| = 6$ V for 10 V total in series.

Why the others are wrong:

• A: Underestimates difference, ignoring full voltage split.
• B: Matches neither $V_X$ nor partial drop.
• D: Overestimates, as if Y had higher share than 4:1 ratio allows.

Final answer: C