📚 Prelims PP: I-V Characteristics | 考前真题：I-V 特性
In A-Level Physics, questions on I-V characteristics often appear in preliminary papers because they test both experimental understanding and graph interpretation. This revision article covers the core ideas, common components, practical skills and typical exam traps you need to master.
在 A-Level 物理中，I-V 特性题目经常出现在考前真题（prelim papers）里，因为它们同时考查实验理解与图像分析能力。本篇文章梳理核心概念、常见元件、实验技能和典型失分点。
1. What I-V Characteristics Mean | 什么是 I-V 特性
An I-V characteristic is a graph of current I through a component against the potential difference V across it. The shape of the graph tells you whether the component obeys Ohm's law and how its resistance changes.
I-V 特性是指通过元件的电流 I 与元件两端电势差 V 的关系图。图像形状可以说明元件是否遵循欧姆定律，以及电阻如何变化。
the x-axis and I on the y-axis, so the gradient of a straight-line section is ΔI/ΔV = 1/R.
严格来说，通常把 V 放在 x 轴、I 放在 y 轴，因此直线段的斜率 ΔI/ΔV = 1/R。
R = V / I
2. Ohm's Law and Ohmic Conductors | 欧姆定律与欧姆导体
Ohm's law states that, for a conductor at constant temperature, the current I is directly proportional to the potential difference V across it. This means resistance R is constant.
欧姆定律指出，在温度不变的条件下，导体中的电流 I 与两端电势差 V 成正比。这意味着电阻 R 保持不变。
Ohmic conductors, such as a metal wire at steady temperature, give a straight line through the origin on an I-V graph.
欧姆导体（例如温度稳定的金属丝）的 I-V 图像是一条过原点的直线。
I = V / R
3. The I-V Graph of a Fixed Resistor | 定值电阻的 I-V 图
For a fixed resistor at constant temperature, the I-V graph is a straight line through the origin with constant gradient. Doubling the p.d. doubles the current.
对于温度恒定的定值电阻，I-V 图是一条过原点的直线，斜率恒定。电压加倍，电流也加倍。
If the resistor heats up significantly, its graph may curve because the resistance of many metals increases with temperature.
如果电阻明显发热，图像可能弯曲，因为很多金属的电阻随温度升高而增大。
4. Filament Lamp: Non-Ohmic Behaviour | 白炽灯：非欧姆行为
A filament lamp is non-ohmic because its temperature changes as current increases. The metal filament heats up, its ions vibrate more, and the resistance increases.
白炽灯是非欧姆元件，因为电流增大时温度会变化。金属灯丝受热后离子振动加剧，电阻增大。
The I-V graph is a curve through the origin that becomes shallower at higher p.d., showing increasing resistance. The graph is symmetrical for positive and negative p.d. because reversing direction does not change the heating effect.
其 I-V 图是过原点的曲线，在较高电压下变平缓，表明电阻增大。正负电压下的图像关于原点对称，因为反向连接不会改变热效应。
5. Semiconductor Diode: Forward and Reverse Bias | 半导体二极管：正向与反向偏置
A semiconductor diode only conducts easily in forward bias. In forward bias, a small p.d. above about 0.6 V for silicon causes a sharp rise in current. In reverse bias, current is almost zero until breakdown voltage.
半导体二极管只在正向偏置时容易导通。对硅二极管，正向电压约超过 0.6 V 后电流急剧上升；反向偏置时电流几乎为零，直到击穿电压。
Its I-V graph is highly asymmetrical: near-zero current for reverse p.d. and a steep forward curve after the threshold voltage.
其 I-V 图高度不对称：反向电压下电流几乎为零，超过阈值电压后正向曲线非常陡。
6. Thermistor and LDR: Changing Resistance | 热敏电阻与光敏电阻：变化的电阻
A thermistor is a temperature-dependent resistor. For a negative temperature coefficient (NTC) thermistor, resistance decreases as temperature rises, so at a fixed p.d. the current increases when it is heated.
热敏电阻是一种随温度变化的电阻。负温度系数（NTC）热敏电阻的电阻随温度升高而减小，因此在固定电压下加热时电流增大。
A light-dependent resistor (LDR) has resistance that decreases as light intensity increases. Both are non-ohmic because their resistance is controlled by external conditions, not simply by V and I.
光敏电阻（LDR）的电阻随光照强度增大而减小。两者都是非欧姆元件，因为电阻由外界条件控制，而不仅仅取决于 V 和 I。
In I-V experiments, they show a family of straight-line graphs through the origin if temperature or light is kept constant, with different gradients at different conditions.
在 I-V 实验中，如果保持温度或光照不变，它们会显示一组过原点的直线，不同条件下的斜率不同。
7. Required Practical: Circuit and Data | 必做实验：电路与数据
The standard circuit uses a variable resistor or potential divider to vary the p.d. across the component, with an ammeter in series and a voltmeter in parallel.
标准电路使用可变电阻或分压器改变元件两端的电压，电流表串联，电压表并联。
Use the potential divider arrangement when you need to obtain p.d. values from zero upwards, especially for a diode where the forward threshold is small.
当需要从零开始调节电压时，尤其是二极管正向阈值较小时，应使用分压器接法。
Take pairs of V and I readings, reverse the connections to obtain negative values, and plot V on the x-axis and I on the y-axis.
记录成对的 V 和 I 读数，交换连接以获得负值，并以 V 为 x 轴、I 为 y 轴作图。
8. Common Prelim PP Pitfalls | 考前真题常见失分点
One common error is plotting I on the x-axis and V on the y-axis. In A-Level I-V graphs, the convention is V on the x-axis and I on the y-axis.
常见错误之一是把 I 放在 x 轴、V 放在 y 轴。在 A-Level 的 I-V 图中，惯例是 V 在 x 轴、I 在 y 轴。
Another error is calling a filament lamp ohmic just because its graph passes through the origin. A component is ohmic only if the whole graph is a straight line of constant gradient.
另一个错误是因为白炽灯的图线经过原点就说它是欧姆元件。只有当整条图线是斜率不变的直线时，元件才是欧姆导体。
Students also confuse gradient with resistance: for a non-linear graph, resistance at a point is V/I, not ΔV/ΔI unless the graph is a straight line.
学生还容易混淆斜率与电阻：对于非线性图像，某点的电阻是 V/I，而不是 ΔV/ΔI，除非图像是直线。
For diodes, forgetting that reverse bias gives almost no current until breakdown can lose marks on graph sketches.
对于二极管，忘记反向偏置时在击穿前电流几乎为零，会在画图题中丢分。
9. Exam Technique: Describing Graphs | 考试技巧：描述图像
When describing an I-V graph, state the shape, the intercept, whether it passes through the origin, symmetry and what the gradient means. Link gradient to resistance only for straight sections.
描述 I-V 图时，要说明形状、截距、是否过原点、对称性以及梯度的意义。只有在直线区段才能把梯度和电阻联系起来。
Use numerical values from the graph where possible, such as threshold voltage for a diode or the p.d. at which a filament starts to curve.
尽可能使用图中的数值，例如二极管的阈值电压，或灯丝开始弯曲时的电压。
For 'state and explain' questions, write the observation first, then the physics cause, such as increased lattice vibrations increasing resistance.
对于 'state and explain' 类问题，先写观察结果，再写物理原因，例如晶格振动加剧导致电阻增大。
10. Worked Example: Finding Resistance from I-V Data | 例题：由 I-V 数据求电阻
Worked example: At a p.d. of 2.0 V, a filament lamp carries a current of 0.25 A. Calculate its resistance at this point.
例题：当电压为 2.0 V 时，一个白炽灯通过的电流为 0.25 A。计算该工作点的电阻。
R = V / I = 2.0 V / 0.25 A = 8.0 Ω
Since the filament is non-ohmic, this is the resistance only at that particular p.d.; at a higher p.d. the resistance will be larger.
由于灯丝是非欧姆元件，这只是该电压下的电阻；在更高电压下电阻会更大。
11. Key Equations and Units | 关键公式与单位
R = V / I
P = VI = I²R = V² / R
Units: potential difference in volts (V), current in amperes (A), resistance in ohms (Ω).
单位：电势差为伏特（V），电流为安培（A），电阻为欧姆（Ω）。
| Component / 元件 | I-V graph / I-V 图 | Resistance behaviour / 电阻变化 |
| Fixed resistor / 定值电阻 | Straight line through origin / 过原点直线 | Constant / 不变 |
| Filament lamp / 白炽灯 | Symmetrical curve, shallower at high V / 高电压下变平缓的对称曲线 | Increases with temperature / 随温度升高而增大 |
| Diode / 二极管 | Asymmetric, forward current after threshold / 不对称，超过阈值后正向导通 | Very high in reverse, low in forward / 反向很大，正向较小 |
12. Summary Checklist | 总结清单
Remember: ohmic means a straight line through the origin at constant temperature; non-ohmic devices such as filament lamps, diodes, thermistors and LDRs require graph analysis at each point.
记住：欧姆意味着在温度不变时图像是过原点的直线；白炽灯、二极管、热敏电阻和光敏电阻等非欧姆元件需要逐点分析图像。
er graph sketches and calculations using R = V/I rather than assuming constant resistance.
练习真题中的画图题和计算题，并使用 R = V/I，而不是默认电阻不变。
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