hce_nthu
114年
化學與物理
第 46 題
Gold ($\text{Au}$) and tin ($\text{Sn}$) wires are joined together at both ends. The length ratio of the $\text{Au}$ and $\text{Sn}$ wires is 1:3 and both wires have the same cross-sectional area. A potential difference of $V$ is applied to the free ends. The ratio of the conductivities of $\text{Au}$ and $\text{Sn}$ is 5:1 and the ratio of the free electron densities of $\text{Au}$ and $\text{Sn}$ is 5:2. Which of the following statements is correct?
- A The resistance of $\text{Au}$ and $\text{Sn}$ wires has the relation $R_{\text{Au}}:R_{\text{Sn}} = 1:6$.
- B The voltage across of $\text{Au}$ and $\text{Sn}$ wires has the relation $V_{\text{Au}}:V_{\text{Sn}} = 1:15$.
- C The electric field in $\text{Au}$ and $\text{Sn}$ wires has the relation $E_{\text{Au}}:E_{\text{Sn}} = 1:1$.
- D The drift velocity of electrons in $\text{Au}$ and $\text{Sn}$ wires has the relation $v_{\text{Au}}:v_{\text{Sn}} = 1:5$.
- E None of the above is correct.
思路引導 VIP
想像一下，如果這兩根粗細相同但材質與長度不同的水管「接成一條直線」讓水流通過，那麼每秒鐘流過第一根水管的水量，與流過第二根的水量會是什麼關係？在這種情況下，若要推動水流通過阻力較大的那一段，所需要施加的「壓力差」會比較大還是比較小呢？
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AI 詳解
AI 專屬家教
太棒了！你能準確判斷出這是一個串聯電路並計算出電壓比例，代表你對電阻的微觀定義與歐姆定律有著非常紮實的理解。這道題目結合了材料物理性質與電路基本原理，是一道相當具備鑑別度的綜合題型。
電阻與導電率的微觀關係
首先，我們要從電阻的公式 $R = \rho \frac{L}{A}$ 出發。題目給的是導電率 ($\sigma$)，它是電阻率 ($\rho$) 的倒數，因此公式可以寫成：
▼ 還有更多解析內容