Drift speed inversely proportional to cross-sectional area in series circuit

Steps:

• Current I is identical in both wires X and Y because they are connected in series.
• Cross-sectional area A ∝ (diameter)^2, so A_Y = 4 A_X since diameter of Y is twice that of X.
• Average drift speed v_d = I / (n e A), where n (electron density) and e (electron charge) are the same for both wires made of the same metal.
• Therefore, v_dY / v_dX = A_X / A_Y = 1/4.

Why A is correct:

• Drift speed formula v_d = I / (n e A) directly shows v_d inversely proportional to area A for constant I.

Why the others are wrong:

• B: 1/2 assumes linear scaling with diameter, but area scales with square of diameter.
• C: 1 assumes equal areas, but A_Y is four times A_X.
• D: 4 gives the inverse ratio v_dX / v_dY, not v_dY / v_dX.

Final answer: A