AP物理2 电容 — AP 物理 2

1. 什么是电容？ ★☆☆☆☆ ⏱ 2 min

电容描述了一对相互分开的导体储存分离电荷，进而储存电势能的能力。它占AP物理2考试总分的2-3%，在选择题（MCQ）和简答题（FRQ）中都会考查，常结合电场/电势概念或电路问题出题。

2. 平行板电容 ★★☆☆☆ ⏱ 4 min

AP物理2考试中最常考的电容器结构是平行板电容器：两块相同的平行导电极板，间距$d$均匀，极板间为真空或空气。

C = \frac{\epsilon_0 A}{d}

Exam tip: 代入电容公式前一定要先将单位转换为国际单位制；极板间距通常以毫米或微米为单位给出，忘记转换会导致答案偏差3或6个数量级，这是选择题中常见的陷阱。

3. 电容器的组合 ★★★☆☆ ⏱ 4 min

电容器在电路中几乎都是组合使用的。需要记住的关键点：电容器的组合规则与电阻的组合规则相反。并联电容器的所有极板电势差相同，而串联电容器的所有极板储存电荷量相同。

For capacitors in parallel, total charge stored is the sum of individual charges. Substituting $Q = C V$ and canceling the common $V$ gives:

C_{eq, parallel} = C_1 + C_2 + ... + C_n

For capacitors in series, total potential difference across the combination is the sum of individual potential differences. Substituting $V = Q/C$ and canceling the common $Q$ gives:

\frac{1}{C_{eq, series}} = \frac{1}{C_1} + \frac{1}{C_2} + ... + \frac{1}{C_n}

Exam tip: 记住电容组合规则与电阻组合规则相反，混淆规则是本知识点最常见的错误。

4. 电介质与电容器储能 ★★★☆☆ ⏱ 4 min

Most practical capacitors use an insulating material called a dielectric between their plates. Dielectrics increase capacitance by a dimensionless factor called the dielectric constant $\kappa$, where $\kappa > 1$ for all insulating materials. Dielectrics polarize in the electric field between plates, reducing the net electric field for a given stored charge, which increases capacitance per the definition $C = Q/V$.

When a dielectric fills the entire gap between plates of a parallel-plate capacitor, the capacitance becomes:

C = \kappa \frac{\epsilon_0 A}{d}

Work done to separate charge on a capacitor is stored as electric potential energy. There are three equivalent forms for stored energy:

U = \frac{1}{2} Q V = \frac{1}{2} C V^2 = \frac{Q^2}{2 C}

The energy is stored in the electric field between the plates, with energy density (energy per unit volume):

u = \frac{1}{2} \kappa \epsilon_0 E^2

Exam tip: 插入/取出电介质前，一定要先检查电容器是否还连接在电池上（$V$恒定）还是已经断开（$Q$恒定）。这会改变各物理量的变化规律，以及你应该使用的公式。