Electrical Resistance | 电阻

📚 Electrical Resistance | 电阻

Electrical resistance is a central concept in current electricity. It describes how much a component opposes the flow of charge and determines the current that results from a given potential difference.

电阻是电流学中的一个核心概念。它描述一个元件对电荷流动的阻碍程度，并决定在给定电势差下产生的电流大小。

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1. What is Electrical Resistance? | 什么是电阻？

Resistance R is defined as the ratio of potential difference V across a conductor to the current I through it. The SI unit of resistance is the ohm (Ω). One ohm means a potential difference of one volt drives a current of one ampere.

电阻 R 定义为导体两端电势差 V 与通过导体的电流 I 之比。电阻的 SI 单位是欧姆（Ω）。1 欧姆表示 1 伏特电势差产生 1 安培电流。

R = V / I

For a fixed potential difference, a larger resistance gives a smaller current. Resistance arises from collisions between free charge carriers and the vibrating lattice ions inside a material.

在固定电势差下，电阻越大，电流越小。电阻源于自由载流子与材料内部振动晶格离子之间的碰撞。

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2. Ohm’s Law and Ohmic Conductors | 欧姆定律与欧姆导体

Ohm’s law states that, at constant temperature, the current I through a metallic conductor is directly proportional to the potential difference V across it. A conductor that obeys this law is called an ohmic conductor.

欧姆定律指出，在温度恒定的条件下，通过金属导体的电流 I 与其两端电势差 V 成正比。遵守该定律的导体称为欧姆导体。

V = IR

The I-V graph for an ohmic conductor is a straight line through the origin. The gradient gives 1/R, and the resistance is constant as long as temperature does not change significantly.

欧姆导体的 I-V 图像是一条过原点的直线。斜率给出 1/R，只要温度没有显著变化，电阻就保持恒定。

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3. Non-Ohmic Behaviour | 非欧姆行为

Many components do not obey Ohm’s law. A filament lamp has an I-V curve that bends at high potential difference because its metal filament heats up and its resistance increases.

许多元件不服从欧姆定律。白炽灯的 I-V 曲线在高电势差时弯曲，因为金属灯丝升温，电阻增大。

A semiconductor diode conducts very little in reverse bias and conducts strongly in forward bias above the threshold voltage. Its resistance is therefore very high in one direction and very low in the other.

半导体二极管在反向偏置时几乎不导通，在正向偏置超过阈值电压时强烈导通。因此其电阻在一个方向很大，在另一方向很小。

A negative temperature coefficient (NTC) thermistor shows decreasing resistance as temperature increases. This property makes it useful in temperature sensing circuits.

负温度系数（NTC）热敏电阻随温度升高电阻下降。这一特性使其可用于温度传感电路。

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4. Resistivity and Conductivity | 电阻率与电导率

Resistance depends on both the material and the geometry of a conductor. Resistivity ρ is a material property defined by the equation R = ρL/A, where L is length and A is cross-sectional area.

电阻取决于导体的材料和几何形状。电阻率 ρ 是由方程 R = ρL/A 定义的材料属性，其中 L 是长度，A 是横截面积。

R = ρL / A

The SI unit of resistivity is the ohm metre (Ω m). Conductivity σ is the reciprocal of resistivity, σ = 1/ρ, and has units of siemens per metre (S m⁻¹).

电阻率的 SI 单位是欧姆米（Ω m）。电导率 σ 是电阻率的倒数，σ = 1/ρ，单位为西门子每米（S m⁻¹）。

Metals have very low resistivity, insulators have very high resistivity, and semiconductors lie in between.

金属的电阻率很低，绝缘体的电阻率很高，半导体介于两者之间。

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5. Factors Affecting Resistance | 影响电阻的因素

From R = ρL/A, doubling the length of a wire doubles its resistance, while doubling the cross-sectional area halves its resistance. The material itself also determines resistivity.

根据 R = ρL/A，导线长度加倍会使电阻加倍，而横截面积加倍会使电阻减半。材料本身也决定电阻率。

Temperature changes resistance as well. For most metals, resistance increases with temperature because lattice ion vibrations become more intense. In semiconductors, resistance usually decreases with increasing temperature because more charge carriers are released.

温度也会改变电阻。对大多数金属，电阻随温度升高而增大，因为晶格离子振动加剧。在半导体中，电阻通常随温度升高而减小，因为释放出更多载流子。

• Longer wire → higher R
• Thicker wire → lower R
• Higher temperature in metals → higher R

These relationships are essential when designing heating elements, transmission lines and sensing devices.

这些关系在设计加热元件、输电线路和传感装置时至关重要。

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6. Temperature Dependence of Resistance | 电阻的温度依赖

In metals, conduction electrons collide more frequently with lattice ions when temperature rises, so the drift velocity decreases and resistance increases. Over a moderate temperature range, the change is approximately linear.

在金属中，温度升高时传导电子与晶格离子碰撞更频繁，因此漂移速度降低，电阻增大。在中等温度范围内，这种变化近似线性。

R = R₀(1 + αΔT)

Here R₀ is the original resistance, α is the temperature coefficient of resistance, and ΔT is the change in temperature.

其中 R₀ 是初始电阻，α 是电阻温度系数，ΔT 是温度变化量。

For thermistors and many semiconductors, increasing temperature releases more charge carriers, so resistance falls even though lattice vibrations increase. Superconductors show an abrupt drop to zero resistance below a critical

Published by TutorHao | A-Level Physics Revision Series | aleveler.com

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