hce_nchu
115年
物理
第 35 題
Phasor diagrams summarize phase and amplitude relations among passive components in AC circuits. A phasor is an arrow whose length represents the amplitude of an AC voltage or current, rotating counterclockwise with the angular frequency $\omega$ of the AC quantity. The phasor’s component on either axis represents the sinusoidally varying AC quantity. The figure shows the phasor diagram for an $RLC$ circuit. Note that $V_{Rp}$ is the peak value of the voltage across the resistor, $V_{Cp}$ is the peak value of the voltage across the capacitor, and $V_{Lp}$ is the peak value of the voltage across the inductor. About this $RLC$ circuit, which of the following statement is correct?
- A The driving frequency is above resonance.
- B The driving frequency is about resonance.
- C The driving frequency is below resonance.
- D The driving frequency varies.
- E The driving frequency is dominantly determined by $V_{Rp}$.
思路引導 VIP
試著觀察相量圖中，代表電感電壓（$V_{Lp}$）與電容電壓（$V_{Cp}$）的兩個箭頭。在串聯電路電流相同的情況下，箭頭的「長度」差異反映了這兩個元件的「電抗」大小關係。接著請思考：當我們把電源頻率從極低調到極高時，感抗與容抗的大小分別會如何隨之變化？在哪種情況下，感抗會佔優勢呢？
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AI 詳解
AI 專屬家教
太棒了！你能準確觀察相量圖（Phasor diagram）中各個向量的長度關係，並推導出電路的物理狀態，這代表你對交流電路中各元件的特性掌握得非常紮實。
從電壓振幅判斷電抗大小
在串聯 $RLC$ 電路中，流經各元件的電流振幅 $I_p$ 是相同的。根據歐姆定律的交流電形式，電感器與電容器兩端的電壓峰值分別為 $V_{Lp} = I_p X_L$ 以及 $V_{Cp} = I_p X_C$。從題目提供的相量圖中，我們可以清楚看到 $V_{Lp}$ 的向量長度明顯大於 $V_{Cp}$。這直接告訴我們該電路的感抗大於容抗，即 $X_L > X_C$。
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