Resistance, Resistivity, and Ohm's Law · 电阻、电阻率与欧姆定律
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| resistance/rɪˈzɪstəns/ | 电阻 | diàn zǔ |
| Ohm's law/əʊmz lɔː/ | 欧姆定律 | ōu mǔ dìng lǜ |
| ohm/əʊm/ | 欧姆 | ōu mǔ |
| resistivity/ˌriːzɪˈstɪvəti/ | 电阻率 | diàn zǔ lǜ |
Some components let charge through easily — others fight it
- Push the same voltage through a thin wire and a thick one; the thin one lets less current through.
- Every component resists the flow of charge to some degree.
- That opposition is its resistance 电阻, and it sets how much current a voltage produces.
- The rule linking them for many materials is Ohm's law 欧姆定律.
有些元件让电荷轻松通过——有些则阻挡它
- 用同样的电压推过一根细导线和一根粗导线;细的让通过的电流更少。
- 每个元件都在某种程度上阻碍电荷的流动。
- 那种阻碍就是它的电阻,它决定一个电压能产生多大电流。
- 把它们联系起来的规则,对许多材料而言就是欧姆定律。
Ohm's law
- Resistance is voltage divided by current: $R = \dfrac{V}{I}$, or rearranged $V = IR$.
- Its unit is the ohm 欧姆 ($\Omega$).
- For an ohmic component (like a metal resistor at constant temperature), $R$ is constant.
- Then voltage and current are proportional — a straight line through the origin.
欧姆定律
- 电阻是电压除以电流:$R = \dfrac{V}{I}$,或变形为 $V = IR$。
- 它的单位是欧姆($\Omega$)。
- 对欧姆性元件(如恒温下的金属电阻),$R$ 是常数。
- 那时电压和电流成正比——一条过原点的直线。
V–I of components · 元件的V–I特性
Compare the straight line of a resistor with the curves of a lamp and a diode. · 比较电阻的直线与灯泡和二极管的曲线。
A resistor carries $0.5\ \text{A}$ from a $6\ \text{V}$ supply. What is its resistance, in $\Omega$? · 一个电阻器承载 $0.5\ \text{A}$ 来自 $6\ \text{V}$ 电源。其电阻是多少，单位为 $\Omega$?
$R = V/I = 6/0.5 = 12\ \Omega$.
Which expresses Ohm's law? · 哪个选项表达了欧姆定律？
$V = IR$ — voltage equals current times resistance. · $V = IR$ — 电压等于电流乘以电阻。
What sets a wire's resistance
- A wire's resistance is $R = \dfrac{\rho L}{A}$.
- Longer wire ($L$) ⇒ more resistance; thicker wire (bigger area $A$) ⇒ less resistance.
- $\rho$ is the resistivity 电阻率, a property of the material (copper is low, nichrome is high).
- So resistance depends on the material and the shape of the conductor.
什么决定导线的电阻
- 一根导线的电阻是 $R = \dfrac{\rho L}{A}$。
- 越长的导线($L$)⇒ 电阻越大;越粗的导线(面积 $A$ 越大)⇒ 电阻越小。
- $\rho$ 是电阻率,材料的一种性质(铜低,镍铬合金高)。
- 所以电阻取决于材料和导体的形状。
Making a wire longer (same material and thickness) changes its resistance how? · 使一根导线变长（材料相同且粗细不变）会如何改变其电阻？
$R = \rho L / A$: a longer $L$ gives a larger resistance. · $R = \rho L / A$：更长的$L$给出更大的电阻。
The material property in $R = \rho L / A$ is called the . · $R = \rho L / A$中的材料属性被称为。
Resistivity $\rho$ is an intrinsic property of the material. · 电阻率$\rho$是材料的固有属性。
Select all · 所有 ways to increase a wire's resistance. · 选择所有增加导线电阻的方法。
$R = \rho L / A$ rises with length, resistivity, and thinness. Thicker wire lowers $R$. · $R = \rho L / A$随长度、电阻率和细度增加。较粗的导线会降低$R$。
Not everything is ohmic
- A filament lamp heats up as current rises, so its resistance increases — a curved graph.
- A diode lets current flow one way but blocks the other — very non-ohmic.
- For these, $R = V/I$ still defines resistance at each point, but it isn't constant.
- Ohm's law ($V \propto I$) holds only when $R$ stays fixed.
并非一切都是欧姆性的
- 灯丝灯泡随电流上升而变热,所以它的电阻增大——图是弯曲的。
- 二极管让电流单向流动而阻挡另一方向——非常非欧姆。
- 对这些,$R = V/I$ 仍定义每一点的电阻,但它不是常数。
- 欧姆定律($V \propto I$)只在 $R$ 保持不变时成立。
A filament lamp is non-ohmic: its resistance rises as it heats up, so its V–I graph curves. · 灯丝灯泡是非欧姆性的：随着温度升高，其电阻增大，因此其V–I图线呈曲线状。
The heating filament's resistance increases with current, bending the graph. · 发热灯丝的电阻随电流增加而增大，导致图线弯曲。
Ohm's law ($V = IR$ with constant $R$) applies only to ohmic components at steady temperature. A filament lamp and a diode are non-ohmic — their resistance changes, so their $V$–$I$ graphs are not straight lines.
欧姆定律($V = IR$ 且 $R$ 恒定)只适用于恒温下的欧姆性元件。灯丝灯泡和二极管是非欧姆的——它们的电阻会变,所以它们的 $V$–$I$ 图不是直线。
A resistor carries $0.5\ \text{A}$ when connected to a $6\ \text{V}$ supply. Find its resistance.
- $R = \dfrac{V}{I} = \dfrac{6}{0.5} = 12\ \Omega$.
Double the voltage to $12\ \text{V}$ and (if ohmic) the current doubles to $1\ \text{A}$.
一个电阻接到 $6\ \text{V}$ 电源时通过 $0.5\ \text{A}$。求它的电阻。
- $R = \dfrac{V}{I} = \dfrac{6}{0.5} = 12\ \Omega$。
把电压加倍到 $12\ \text{V}$,(若为欧姆性)电流加倍到 $1\ \text{A}$。
Resistance $R = \dfrac{V}{I}$ (in ohms) opposes current; for an ohmic component $V = IR$ is a straight line. A wire's resistance is $R = \dfrac{\rho L}{A}$ — more for a long thin wire. Non-ohmic parts (lamps, diodes) have a changing resistance.
电阻 $R = \dfrac{V}{I}$(单位欧姆)阻碍电流;对欧姆性元件 $V = IR$ 是一条直线。一根导线的电阻是 $R = \dfrac{\rho L}{A}$——又长又细的导线电阻更大。非欧姆元件(灯泡、二极管)的电阻会变化。