电阻率、电阻网络与电容Resistivity, networks & capacitors
这类题在近年 Section 1 中反复出现。本组五题共 18 分，单题 3–5 分；主要失分点是截面积变化、等势支路的判断，以及把恒压过程和恒电荷过程混在一起。先判断结构和约束，再代入公式。These topics recur in recent Section 1 papers. This set contains five questions worth 18 marks, with 3–5 marks each. Common losses come from changing cross-sectional area, identifying equipotential branches, and confusing fixed voltage with fixed charge. Identify the structure and constraints before substituting numbers.
1电阻由材料与几何共同决定Resistance depends on material and geometry
ρ 是材料电阻率，D 是质量密度。相同材料的两根线，可以用质量消去未知截面积。ρ is resistivity and D is mass density. For two wires of the same material, mass can eliminate unknown area.
先统一长度、质量和面积的单位。Convert lengths, masses and areas to consistent units first.
2看节点，再做串并联Inspect nodes before combining resistors
串联元件流过相同电流，并联元件两端电压相同。对称性可以找出等势点；无限网络可用自相似列方程。Series elements carry the same current; parallel elements have the same voltage. Symmetry identifies equipotential nodes, while infinite networks suggest self-similarity.
等势点之间电流为零，但不能只凭图形相近就删线。Equal potentials imply zero current; similar-looking positions alone do not justify removing a wire.
3电容：先问电压还是电荷不变Capacitors: what remains fixed?
电源连接时通常保持电压；隔离时保持电荷。漏电电容例外：电荷会经过并联漏电电阻逐渐流失。电容并联电压相同，串联时各电容新增的电荷量相同。An attached ideal supply holds voltage fixed; isolation holds charge fixed. A leaky capacitor loses charge through a parallel resistance. Parallel capacitors share voltage; series capacitors receive equal charge increments.
C_parallel = ΣCᵢ; 1/C_series = Σ(1/Cᵢ)
Q_dis(t) = Q₀e−t/RC; Q_charge(t) = Q_∞(1 − e−t/τ)
τ 使用电容看到的等效电阻；漏电模型的充电与放电路径不同。For τ use the resistance seen by C; charging and disconnected discharge have different paths in the leaky model.
| 子题型Sub-type | 识别特征Clue | 核心步骤Core step | 真题Question |
|---|---|---|---|
| 电阻率与质量Resistivity and mass | 同种材料Same material | 消去截面积Eliminate area | 2023 (g) |
| 对称网络Symmetric network | 相对角与中心Opposite corners and centre | 找等势点Find equal potentials | 2024 (l) |
| 无限树Infinite tree | 反复二叉Repeated binary splitting | 写自相似方程Use self-similarity | 2025 (h) |
| 漏电与 RCLeakage and RC | 充电受限、断开后漏电Limited charging; leakage when disconnected | 分压，再用指数衰减Voltage divider, then exponential decay | 2020 (q) |
| 电容能量Capacitor energy | 连接后再断开Connected, then disconnected | 分别固定 V、QFix V, then Q | 2021 (s) |