📚 Comparing Capacitors and Resistors | 电容器与电阻器的比较
In A-Level physics, capacitors and resistors are two essential passive components that appear in nearly every circuit. Although they are often taught together, they store and control energy in fundamentally different ways. This article compares their definitions, equations, circuit behaviour, and applications to help you avoid common confusions in the CIE examination.
在A-Level物理中，电容器和电阻器是两种基本无源元件，几乎出现在每一个电路中。虽然它们常常一起学习，但它们在储能和控制能量的方式上有着根本区别。本文将从定义、公式、电路行为和应用等方面进行比较，帮助你在CIE考试中避免常见混淆。
1. Basic Definitions and Circuit Symbols | 基本定义与电路符号
A resistor is a component that opposes the flow of electric current, converting electrical energy into heat. An ideal resistor obeys Ohm’s law, V = IR, where V is the potential difference across it, I is the current through it, and R is its resistance.
电阻器是阻碍电流流动的元件，将电能转化为热能。理想电阻遵循欧姆定律 V = IR，其中 V 是它两端的电势差，I 是通过它的电流，R 是它的电阻。
A capacitor consists of two conducting plates separated by an insulator called a dielectric. It stores electric charge Q proportional to the voltage V across it, so Q = CV, where C is the capacitance.
电容器由被绝缘体（称为电介质）隔开的两块导体板组成。它储存的电荷 Q 与两端电压 V 成正比，即 Q = CV，其中 C 是电容。
In circuit diagrams, a resistor is drawn as a rectangle (IEC standard) or a zigzag line (ANSI standard); a capacitor is drawn as two parallel lines representing the plates.
在电路图中，电阻器通常画成矩形（IEC标准）或锯齿线（ANSI标准）；电容器画成两条平行线表示极板。
2. Key Equations and Units | 关键公式与单位
Resistance is measured in ohms (Ω), and capacitance is measured in farads (F). A one-farad capacitor stores one coulomb of charge when the voltage across it is one volt.
电阻的单位是欧姆（Ω），电容的单位是法拉（F）。当电容器两端电压为1伏特时，1法拉的电容储存1库仑的电荷。
For a resistor, the current-voltage relationship and the rate of energy dissipation are given by:
对于电阻器，电流-电压关系以及能量耗散速率由以下公式给出：
V = IR, P = I²R = VI
For a capacitor, the charge stored and the capacitance of a parallel-plate capacitor are:
对于电容器，储存的电荷和平行板电容器的电容为：
C = Q/V, C = εA/d
where ε is the permittivity of the dielectric, A is the plate area, and d is the plate separation.
其中 ε 是电介质的介电常数，A 是极板面积，d 是极板间距。
The energy stored in a charged capacitor is:
充电电容器储存的能量为：
E = ½CV²
3. I-V Characteristics | I-V特性
For a resistor at constant temperature, the current is directly proportional to the voltage, so the I–V graph is a straight line through the origin. This is for ohmic conductors in the linear region.
对于恒温下的电阻器，电流与电压成正比，因此 I–V 图是一条通过原点的直线。这是在欧姆导体的线性区域内。
For a capacitor, the current is proportional to the rate of change of voltage:
对于电容器，电流与电压的变化率成正比：
I = C dV/dt
In a steady direct current (DC) circuit, dV/dt = 0, so once the capacitor is fully charged, no steady current flows through it; it acts as an open circuit. In contrast, a resistor permits a constant current under a steady voltage.
在稳定的直流（DC）电路中，dV/dt = 0，因此电容器充满电后稳态电流为零，相当于开路。相比之下，电阻器在稳定电压下允许恒定电流通过。
4. Behaviour in DC Circuits | 直流电路行为
When a DC voltage is suddenly applied to a resistor, the current immediately reaches its steady value V/R, because there is no time dependence.
当直流电压突然施加到电阻器上时，电流立即达到稳态值 V/R，因为不存在时间依赖关系。
When a capacitor is connected to a battery through a resistor, the capacitor voltage rises exponentially towards the supply voltage. The charging current is initially at its maximum value V/R and then decays to zero. The capacitor voltage cannot change instantaneously, so at t = 0 it behaves like a short circuit for current, and after a long time it behaves like an open circuit.
当电容器通过电阻器连接到电池时，电容器电压按指数规律上升到电源电压。充电电流初始达到最大值 V/R，然后衰减到零。电容器电压不能瞬间突变，因此 t = 0 时它对于电流表现为短路，长时间后表现为开路。
5. Series and Parallel Combinations | 串联与并联
The combination rules for resistors and capacitors are opposite. This is a common source of confusion in exams.
电阻和电容的串并联规则恰好相反，这是考试中常见的易混淆点。
For resistors in series, the total resistance is the sum:
电阻串联时，总电阻等于各电阻之和：
R_total = R₁ + R₂ + R₃ + …
For resistors in parallel, the reciprocal of the total resistance is the sum of reciprocals:
电阻并联时，总电阻的倒数等于各电阻倒数之和：
1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …
For capacitors in series, the reciprocal of the total capacitance is the sum of reciprocals:
电容器串联时，总电容的倒数等于各电容倒数之和：
1/C_total = 1/C₁ + 1/C₂ + 1/C₃ + …
For capacitors in parallel, the total capacitance is the sum:
电容器并联时，总电容等于各电容之和：
C_total = C₁ + C₂ + C₃ + …
The reason is that parallel capacitors increase the effective plate area, while series capacitors have the same charge but a larger overall voltage, reducing the effective capacitance.
原因在于并联电容器增大了有效极板面积，而串联电容器电荷相同但总电压增大，从而减小了有效电容。
6. Time Constant and Transient Response | 时间常数与瞬态响应
When a resistor and capacitor are in series, the circuit is called an RC circuit. The product of resistance and capacitance defines the time constant:
当电阻器和电容器串联时，这个电路称为RC电路。电阻和电容的乘积定义了时间常数：
τ = RC
During charging, the voltage across the capacitor at time t is:
充电过程中，电容两端电压随时间 t 的变化为：
V_C(t) = V₀(1 − e^(−t/τ))
The corresponding charging current is:
相应的充电电流为：
I(t) = (V₀/R)e^(−t/τ)
During discharging, the voltage across the capacitor decays as:
放电过程中，电容器两端电压按以下规律衰减：
V_C(t) = V₀ e^(−t/τ)
After one time constant, the voltage changes by about 63.2% of the remaining difference. In an RC circuit, the resistor controls the rate of charging; the capacitor stores the energy.
经过一个时间常数，电压约改变剩余差值的63.2%。在RC电路中，电阻控制充电速率，电容储存能量。
7. Energy Storage vs Energy Dissipation | 储能与耗能
A capacitor stores energy in the electric field between its plates, and this energy can be returned to the circuit later. The stored energy is given by:
电容器在极板间的电场中储存能量，该能量之后可以释放回电路。储存的能量由下式给出：
E = ½CV²
A resistor dissipates electrical energy irreversibly as heat. The power dissipated is:
电阻器将电能不可逆地耗散为热能。耗散功率为：
P = I²R = VI
The fundamental distinction is that an ideal capacitor does not lose energy, while an ideal resistor cannot store energy. In practical circuits, capacitors are used for temporary energy storage, whereas resistors convert energy into a form that cannot be reused by the circuit.
根本区别在于理想电容器不损耗能量，而理想电阻器不能储存能量。在实际电路中，电容器用于暂时储存能量，而电阻器将能量转化为电路无法再利用的形式。
8. Phase Relationships in AC Circuits | 交流电路中的相位关系
In an alternating current (AC) circuit, a resistor obeys Ohm’s law at every instant, so the current and voltage are in phase with each other.
在交流（AC）电路中，电阻器在任何瞬间都服从欧姆定律，因此电流与电压同相。
For a capacitor, the current is proportional to dV/dt, so the current
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