📚 IB Physics: Definition and Calculation of Electric Current | IB物理：电流的定义与计算方法
In the IB Physics curriculum, electric current is one of the most fundamental concepts bridging mechanics, electromagnetism, and circuit analysis. This article provides a comprehensive exploration of how current is defined, measured, and calculated, tailored to the IB Diploma Programme syllabus.
在IB物理课程中，电流是连接力学、电磁学与电路分析的最基本概念之一。本文将围绕IB文凭课程大纲，全面探讨电流的定义、测量与计算方法。
1. What is Electric Current? | 什么是电流？
Electric current is defined as the rate of flow of electric charge through a given cross-sectional area of a conductor. In formal terms, it is the amount of charge passing a point per unit time.
电流的定义是电荷通过导体某一横截面的流动速率。严格来说，它是单位时间内通过某一点的电荷量。
The SI unit of electric current is the ampere (A), named after French physicist André-Marie Ampère. One ampere equals one coulomb of charge passing per second.
电流的国际单位制（SI）单位是安培（A），以法国物理学家安德烈-马里·安培命名。1安培等于每秒通过1库仑的电荷量。
I = ΔQ / Δt
where I is the current in amperes (A), ΔQ is the charge in coulombs (C), and Δt is the time interval in seconds (s).
其中 I 为电流（单位：安培 A），ΔQ 为电荷量（单位：库仑 C），Δt 为时间间隔（单位：秒 s）。
2. Charge Carriers in Conductors | 导体中的电荷载流子
In metallic conductors, electric current is carried by free (delocalised) electrons. Each electron has a charge magnitude of 1.60 × 10⁻¹⁹ C, denoted as the elementary charge e. A copper wire contains approximately 8.5 × 10²⁸ free electrons per cubic metre.
在金属导体中，电流由自由（离域）电子承载。每个电子的电荷量大小为 1.60 × 10⁻¹⁹ 库仑，记为元电荷 e。每立方米铜导线大约含有 8.5 × 10²⁸ 个自由电子。
In electrolytic solutions and ionised gases, charge carriers include both positive and negative ions. In semiconductors, both electrons and electron holes contribute to current flow. The type of carrier affects how current is analysed in different materials.
在电解质溶液和电离气体中，电荷载流子包括正离子和负离子。在半导体中，电子和电子空穴共同参与导电。载流子的类型会影响对不同材料中电流的分析方式。
Charge carrier density (n) is a key parameter: metals have high n values (~10²⁸ m⁻³), intrinsic semiconductors have moderate n values (~10¹⁶ m⁻³), while insulators have extremely low n values.
电荷载流子密度（n）是关键参数：金属具有高 n 值（约 10²⁸ m⁻³），本征半导体具有中等 n 值（约 10¹⁶ m⁻³），而绝缘体的 n 值极低。
3. Conventional Current vs Electron Flow | 传统电流方向与电子流动方向
Conventional current is defined as the direction in which positive charge would flow — from the positive terminal to the negative terminal of a battery. This convention was established by Benjamin Franklin long before the discovery of the electron.
传统电流方向被定义为正电荷流动的方向——从电池的正极流向负极。这一惯例由本杰明·富兰克林在电子被发现之前就已确立。
In reality, electrons in a metal conductor move from the negative terminal to the positive terminal — opposite to conventional current. For calculation purposes in IB Physics, conventional current is always used, as it simplifies circuit analysis and is consistent with electromagnetic field equations.
实际上，金属导体中的电子从负极移动到正极——与传统电流方向相反。在IB物理计算中，始终使用传统电流方向，因为它简化了电路分析，并与电磁场方程保持一致。
A key exam point: Conventional current flows from + to −; electron flow is from − to +.
4. The Equation I = ΔQ / Δt | 电流方程 I = ΔQ / Δt
The fundamental calculation of current involves measuring the charge that passes a point over a time interval. If a steady current flows, the relationship is simply I = Q/t. For varying current, the instantaneous current is given by the derivative: I = dQ/dt.
电流的基本计算涉及测量在时间间隔内通过某一点的电荷量。若电流恒定，关系简化为 I = Q/t。对于变化的电流，瞬时电流由导数给出：I = dQ/dt。
Worked Example 1: A charge of 240 C passes through a filament lamp in 2 minutes. Calculate the current.
示例1：240库仑的电荷在2分钟内通过一只白炽灯。计算电流。
t = 2 × 60 = 120 s; I = 240 / 120 = 2.0 A.
t = 2 × 60 = 120 秒；I = 240 / 120 = 2.0 安培。
Worked Example 2: If a current of 0.50 A flows for 10 minutes, how many electrons pass a given point?
示例2：若0.50安培的电流持续流动10分钟，有多少个电子通过某一点？
Q = I × t = 0.50 × (10 × 60) = 300 C. Number of electrons = 300 / (1.60 × 10⁻¹⁹) = 1.875 × 10²¹ electrons.
Q = I × t = 0.50 × (10 × 60) = 300 库仑。电子数 = 300 / (1.60 × 10⁻¹⁹) = 1.875 × 10²¹ 个电子。
5. Drift Velocity and Current | 漂移速度与电流
Although electrons in a conductor move randomly at high speeds (about 10⁶ m/s), the net drift velocity under an applied electric field is surprisingly small — typically 10⁻⁴ m/s. The current is given by the drift velocity equation:
尽管导体中的电子以高速（约10⁶ m/s）随机运动，但在外加电场作用下的净漂移速度却小得惊人——通常为10⁻⁴ m/s。电流由漂移速度方程给出：
I = n A v q
where n is the charge carrier density (m⁻³), A is the cross-sectional area (m²), v is the drift velocity (m/s), and q is the charge of each carrier (C).
其中 n 为电荷载流子密度（m⁻³），A 为横截面积（m²），v 为漂移速度（m/s），q 为每个载流子的电荷量（C）。
Worked Example 3: A copper wire has a cross-sectional area of 1.0 × 10⁻⁶ m² and carries a current of 2.0 A. Given n = 8.5 × 10²⁸ m⁻³, find the drift velocity.
示例3：一根铜导线横截面积为 1.0 × 10⁻⁶ m²，通有2.0安培电流。已知 n = 8.5 × 10²⁸ m⁻³，求漂移速度。
v = I / (n A q) = 2.0 / (8.5 × 10²⁸ × 1.0 × 10⁻⁶ × 1.60 × 10⁻¹⁹) = 1.47 × 10⁻⁴ m/s.
v = I / (n A q) = 2.0 / (8.5 × 10²⁸ × 1.0 × 10⁻⁶ × 1.60 × 10⁻¹⁹) = 1.47 × 10⁻⁴ m/s。
This explains why a light switch appears “instant” — the electric field propagates at near light speed, while individual electrons drift slowly.
这解释了为什么电灯开关看起来是”瞬间”的——电场以接近光速传播，而单个电子的漂移却很慢。
6. Current Density | 电流密度
Current density, denoted as J, is the current per unit cross-sectional area: J = I / A. It is a vector quantity whose direction is that of conventional current. The SI unit is A/m².
电流密度，记为 J，是单位横截面积上的电流：J = I / A。它是一个矢量，方向与传统电流方向一致。其SI单位是 A/m²。
Current density is particularly useful in analysing non-uniform conductors and semiconductor devices. In terms of drift velocity, J = n q v.
电流密度在分析非均匀导体和半导体器件时特别有用。用漂移速度表示时，J = n q v。
Worked Example 4: A wire of radius 0.50 mm carries 3.0 A. Compute J.
示例4：一根半径0.50毫米的导线通有3.0安培电流。计算 J。
A = π × (0.50 × 10⁻³)² = 7.85 × 10⁻⁷ m²; J = 3.0 / (7.85 × 10⁻⁷) = 3.82 × 10⁶ A/m².
A = π × (0.50 × 10⁻³)² = 7.85 × 10⁻⁷ m²；J = 3.0 / (7.85 × 10⁻⁷) = 3.82 × 10⁶ A/m²。
7. Ohm’s Law and Current | 欧姆定律与电流
Georg Ohm discovered that for many conductors at constant temperature, the current is proportional to the potential difference across the conductor. This is expressed as:
乔治·欧姆发现，在恒定温度下，许多导体的电流与两端的电势差成正比。这表示为：
I = V / R
where V is the potential difference in volts (V), R is the resistance in ohms (Ω). For a fixed resistance, doubling V doubles I.
其中 V 为电势差（单位：伏特 V），R 为电阻（单位：欧姆 Ω）。对于固定电阻，V 加倍则 I 加倍。
In IB examinations, this relationship is crucial for circuit analysis. Note that Ohm’s law applies to ohmic conductors (e.g., metal wires at constant temperature), but not to non-ohmic devices like diodes or filament lamps, which have non-linear I–V characteristics.
在IB考试中，此关系对电路分析至关重要。注意欧姆定律适用于欧姆导体（如恒温金属导线），但不适用于二极管或白炽灯等非欧姆器件，它们的 I–V 特性曲线是非线性的。
When analysing circuits, correctly applying I = V/R requires identifying whether the component is in series (same current, voltage splits) or parallel (same voltage, current splits).
在分析电路时，正确应用 I = V/R 需要判断元件是串联（电流相同，电压分配）还是并联（电压相同，电流分配）。
8. Direct Current vs Alternating Current | 直流电与交流电
Direct current (DC) flows in one constant direction, maintaining a constant polarity. Batteries and solar cells supply DC. In DC circuits, the current value is steady over time, simplifying calculations.
直流电（DC）沿恒定方向流动，保持恒定极性。电池和太阳能电池提供直流电。在直流电路中，电流值随时间稳定，简化了计算。
Alternating current (AC) periodically reverses direction. The standard frequency for AC mains is 50 Hz in many countries (including China and the UK) and 60 Hz in others (like the USA). The time period is T = 1/f.
交流电（AC）周期性改变方向。许多国家（包括中国和英国）的市电标准频率为50 Hz，其他国家（如美国）为60 Hz。周期为 T = 1/f。
For AC, a sinusoidal current is described by I = I₀ sin(ωt), where I₀ is the peak current and ω is the angular frequency (ω = 2πf). The root-mean-square (RMS) value of an AC current is I_rms = I₀ / √2, which represents the equivalent DC value that would dissipate the same power.
对于交流电，正弦电流可表示为 I = I₀ sin(ωt)，其中 I₀ 为峰值电流，ω 为角频率（ω = 2πf）。交流电流的均方根（RMS）值为 I_rms = I₀ / √2，它表示耗散相同功率的等效直流值。
Worked Example 5: If the peak value of AC current is 5.0 A, calculate the RMS current and the average power dissipated in a 10 Ω resistor.
示例5：若交流电的峰值电流为5.0安培，计算RMS电流以及10欧姆电阻上耗散的平均功率。
I_rms = 5.0 / √2 = 3.54 A; P = I_rms² × R = (3.54)² × 10 = 125 W.
I_rms = 5.0 / √2 = 3.54 安培；P = I_rms² × R = (3.54)² × 10 = 125 瓦。
9. Measuring Current: The Ammeter | 测量电流：安培计
An ammeter is used to measure current and must be connected in series with the component whose current is being measured. This ensures the full current flows through the instrument.
安培计用于测量电流，必须与待测电流的元件串联。这确保全部电流流经仪器。
An ideal ammeter has zero resistance so that its insertion does not alter the circuit current. In practice, real ammeters have very low but finite resistance, causing a small voltage drop that is usually negligible.
理想安培计的电阻为零，这样接入时不会改变电路电流。实际上，真实安培计具有很低但有限的电阻，会产生通常可忽略的微小电压降。
When using a digital or analogue ammeter, select an appropriate range to maximise accuracy. Always check the zero reading before starting measurements and record uncertainty information as required by the IB internal assessment guidelines.
使用数字或指针式安培计时，应选择合适的量程以最大化精度。测量前始终检查零点读数，并按照IB内部评估指南记录不确定度信息。
10. Energy and Power in Current Flow | 电流中的能量与功率
When current flows through a component, electrical energy is converted into other forms. The electric power dissipated is given by:
电流通过元件时，电能转化为其他形式的能量。耗散的电功率为：
P = V × I = I² × R = V² / R
For a circuit with current I and voltage V, the energy converted in time t is W = VIt, measured in joules (J). Commercial electricity is measured in kilowatt-hours (kWh), where 1 kWh = 3.6 × 10⁶ J.
对于电流 I 和电压 V 的电路，在时间 t 内转换的能量为 W = VIt，单位为焦耳（J）。商业用电以千瓦时（kWh）计量，其中 1 kWh = 3.6 × 10⁶ J。
Worked Example 6: A 12 V battery drives a 3.0 A current. Determine the power output and the energy delivered in 5 minutes.
示例6：一个12伏电池驱动3.0安培电流。确定功率输出和5分钟内传递的能量。
P = 12 × 3.0 = 36 W; W = 36 × (5 × 60) = 10,800 J = 1.08 × 10⁴ J.
P = 12 × 3.0 = 36 瓦；W = 36 × (5 × 60) = 10,800 焦耳 = 1.08 × 10⁴ 焦耳。
11. Kirchhoff’s Laws and Current | 基尔霍夫定律与电流
Kirchhoff’s Current Law (KCL) states that the total current entering a junction equals the total current leaving that junction. Mathematically: ΣI_in = ΣI_out.
基尔霍夫电流定律（KCL）指出，流入节点的总电流等于流出该节点的总电流。数学表达式：ΣI_in = ΣI_out。
This principle is a direct consequence of charge conservation. In IB problems, students often use KCL to find unknown currents in multi-branch circuits. For example, if 5 A enters a junction and splits into I₁ = 2 A and I₂, then I₂ = 3 A.
该原理是电荷守恒的直接结果。在IB题目中，学生常用KCL求解多支路电路中的未知电流。例如，若5安培进入节点并分流为 I₁ = 2 安培和 I₂，则 I₂ = 3 安培。
Kirchhoff’s Voltage Law (KVL) complements KCL: the sum of the electromotive forces (EMFs) in any closed loop equals the sum of the potential drops. Both laws together provide a systematic method for analysing circuits of arbitrary complexity.
基尔霍夫电压定律（KVL）与KCL互补：任何闭合回路中的电动势（EMF）之和等于电势降之和。两条定律共同为分析任意复杂度的电路提供了系统方法。
12. Common Misconceptions and IB Exam Tips | 常见误解与IB考试建议
Misconception 1: “Current is used up in a circuit.” This is false — charge is conserved; energy is transferred. The same current flows through series components.
误解1：“电流在电路中被消耗掉了。”这是错误的——电荷守恒；被转移的是能量。串联元件中流过的电流相同。
Misconception 2: “Electrons move at the speed of light.” The drift velocity is tiny (10⁻⁴ m/s), but the electric field propagates at roughly 10⁸ m/s, causing the rapid response when a switch closes.
误解2：“电子以光速运动。”漂移速度极小（10⁻⁴ m/s），但电场以约10⁸ m/s的速度传播，导致开关闭合时电路迅速响应。
Misconception 3: “Larger voltage always means larger current.” Not true if resistance changes simultaneously. Always apply I = V/R considering the specific circuit context.
误解3：“电压越大电流必然越大。”如果电阻同时变化，这就不正确。务必结合具体电路条件应用 I = V/R。
Exam tip: Always convert time to seconds; use consistent units; round final answers to 2 or 3 significant figures; and show the substitution step clearly to earn method marks.
考试建议：始终将时间转换为秒；使用一致的单位；最终答案保留2到3位有效数字；清楚地写出代入步骤以获得方法分。
Mastering the definition and calculation of electric current is essential for success in IB Physics. Practice with past-paper questions on drift velocity, RMS current, and Kirchhoff’s laws to build confidence. Remember: every quantity in the IB data booklet — from Q = It to I = nAvq — is a tool for unpacking real-world electrical phenomena.
掌握电流的定义与计算是IB物理成功的关键。通过练习有关漂移速度、RMS电流和基尔霍夫定律的历年真题来建立信心。记住：IB数据手册中的每一个方程——从 Q = It 到 I = nAvq——都是解读真实电学现象的工具。
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