Potential Divider Voltage Formula

Steps:

• Initially, X = Y = R, total resistance 2R, output across Y: V_out = 12 × (R / 2R) = 6V.
• After halving X to 0.5R, total resistance 1.5R, output across Y: V_out = 12 × (R / 1.5R) = 8V.
• Change in output voltage: 8V - 6V = +2V.

Why C is correct:

• Output across unchanged Y increases as its proportion of total resistance rises from 1/2 to 2/3, per the voltage divider formula V_out = V_s × (R_Y / (R_X + R_Y)).

Why the others are wrong:

• A: Incorrect sign and magnitude; assumes decrease across X with wrong value.
• B: Correct magnitude but wrong sign; applies if output measured across X.
• D: Wrong magnitude; likely from misapplying formula, e.g., doubling instead of halving.

Final answer: C