Voltage divider in series circuit

Steps:

• Voltage across 160Ω resistor is total emf minus Vx: 9.0 V - 4.0 V = 5.0 V.
• Current I through circuit is voltage across 160Ω divided by its resistance: I = 5.0 V / 160 Ω = 0.03125 A.
• Resistance R is Vx divided by current: R = 4.0 V / 0.03125 A = 128 Ω.
• This matches option D.

Why D is correct:

• In a series circuit, current is the same through both resistors, and voltages sum to the emf (Kirchhoff's voltage law).

Why the others are wrong:

• A: 320 Ω gives Vx = (320 / 480) × 9 V = 6.0 V, not 4.0 V.
• B: 49 Ω gives Vx = (49 / 209) × 9 V ≈ 2.1 V, not 4.0 V.
• C: 71 Ω gives Vx = (71 / 231) × 9 V ≈ 2.8 V, not 4.0 V.

Final answer: D