Explanation: To operate a vacuum tube filament at its rated specifications from a higher voltage source, a series resistor is required to drop the excess voltage. The filament needs 5 V and draws 0.25 A. When powered by a 6 V battery, the series resistor must drop the difference in voltage: 6 V (source) - 5 V (filament) = 1 V. Since the resistor is in series with the filament, the same current (0.25 A) flows through both. Using Ohm's Law, R = V/I, where R is the resistance, V is the voltage drop across the resistor, and I is the current. Therefore, the necessary resistance is: R = 1 V / 0.25 A = 4 ohms. This value ensures the filament operates at its correct voltage and current, preventing damage from over-voltage. Options B, C, and D would result in different voltage drops, causing the filament to operate outside its specifications.