hce_nthu
112年
化學與物理
第 55 題
As shown in the figure below, an RC circuit consists of a resistor $R$, and two capacitors $C_1$ and $C_2$ (with different capacitance). At $t = 0$, the charges stored on $C_1$ and $C_2$ are $Q_0$ and 0, respectively. And the switch is also closed at $t = 0$.
Which of the following statements is true?
Which of the following statements is true?
- A The charges would go back and forth between $C_1$ and $C_2$ repeatedly.
- B The charge would flow back and forth between $C_1$ and $C_2$, but the amount of charge is getting less and less.
- C When one waits long enough, both capacitors share the same amount of energy.
- D When one waits long enough, the voltage across the resistor becomes zero.
- E When one waits long enough, the charges are neutralized and both the positive and negative charges of the two capacitors are zero.
思路引導 VIP
請試著思考：在開關剛閉合時，電荷之所以會流動，是因為兩側電容器的電壓不同。那麼，當電荷流動到什麼樣的狀態時，電荷會「停止搬家」？而當電荷不再流動時，根據電路基本定律，那個連接兩端的電阻器上還會存在壓降嗎？
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AI 詳解
AI 專屬家教
太棒了！你能精準選出選項 (D)，代表你對 RC 電路進入「穩態」時的物理性質掌握得非常紮實。
電壓平衡與穩態的達成
這道題目的核心在於理解電荷重新分佈的動態過程。當開關在 $t=0$ 閉合時，由於只有 $C_1$ 儲存了電荷 $Q_0$ 而 $C_2$ 電量為零，兩者之間存在電位差（電壓差）。這個電位差會驅動電流流經電阻 $R$，使得電荷從 $C_1$ 流向 $C_2$。隨著時間推移，當兩台電容器的電位達到相等（即 $V_1 = V_2$）時，系統便達到了熱力學上的「穩態」。
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