A capacitor is charging through a resistor from an ideal battery. Which statement best describes the resistor's voltage drop as time increases?
- starts near the battery voltage and decreases toward . (correct answer)
- starts at and increases toward the battery voltage.
- remains constant because the resistor's resistance is constant.
- becomes greater than the battery voltage briefly, then returns.
Explanation: This question tests understanding of resistor-capacitor (RC) circuits. When charging begins, the uncharged capacitor acts like a short circuit with zero voltage, so the entire battery voltage initially appears across the resistor, creating maximum current (I₀ = V_battery/R). As the capacitor charges and its voltage increases, the voltage across the resistor must decrease to maintain Kirchhoff's voltage law (V_battery = V_R + V_C), causing the current and resistor voltage to decay exponentially toward zero. At long times, the capacitor reaches battery voltage, current stops, and the resistor voltage becomes zero. Choice C incorrectly assumes constant resistor voltage, representing the misconception that resistance alone determines voltage drop—in reality, V_R = IR depends on the changing current. To solve charging circuits, apply Kirchhoff's voltage law at any instant to relate component voltages.