Electric Power · 电功率
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| power/ˈpaʊə/ | 功率 | gōng lǜ |
| watt/wɒt/ | 瓦特 | wǎ tè |
| dissipation/ˌdɪsɪˈpeɪʃn/ | 耗散 | hào sàn |
Where does a battery's energy go — and how fast?
- A battery hands energy to charges; the circuit spends it.
- Power 功率 is how fast that energy is delivered or used.
- A bright bulb spends energy quickly; a dim one spends it slowly.
- Power ties current and voltage to heat, light, and motion.
电池的能量去了哪里——有多快?
- 电池把能量交给电荷;电路把它花掉。
- 功率是那份能量被输送或使用的快慢。
- 亮灯泡花能量快;暗灯泡花得慢。
- 功率把电流和电压与热、光、运动联系起来。
Power = current × voltage
- Each charge drops energy $qV$ as it crosses a component.
- Charges arrive at a rate $I$, so the energy per second is $P = IV$.
- Its unit is the watt 瓦特 (1 W $= 1$ J/s).
- Power is simply how many joules leave the source every second.
功率 = 电流 × 电压
- 每个电荷穿过一个元件时降落能量 $qV$。
- 电荷以速率 $I$ 到达,所以每秒的能量是 $P = IV$。
- 它的单位是瓦特(1 W $= 1$ J/s)。
- 功率就是每秒有多少焦耳离开电源。
Power in a resistor · 电阻中的功率
Set the voltage and resistance and watch the current and power that result. · 设定电压和电阻，观察由此产生的电流和功率。
Electric power delivered to a component is: · 输送到某个元件的电功率是：
$P = IV$ — current times voltage, in watts. · $P = IV$ — 电流乘以电压，单位为瓦特。
A device draws $4\ \text{A}$ at $12\ \text{V}$. Find its power (in W). · 一个设备在$4\ \text{A}$时消耗$12\ \text{V}$。求其功率（单位：W）。
$P = IV = 4 \times 12 = 48\ \text{W}$.
The SI unit of power is the . · 功率的SI单位是。
1 watt $= 1$ J/s. · 1瓦特 $= 1$ J/s。
Three forms of the same law
- Combine with Ohm's law to get $P = I^2 R$ and $P = \dfrac{V^2}{R}$.
- Use whichever fits what you know: $I$ and $R$, or $V$ and $R$.
- All three give the same power for an ohmic resistor.
- $P = I^2 R$ shows why a big current heats a wire so strongly.
同一定律的三种形式
- 与欧姆定律结合得到 $P = I^2 R$ 和 $P = \dfrac{V^2}{R}$。
- 用最适合你已知量的那个:$I$ 和 $R$,或 $V$ 和 $R$。
- 对欧姆性电阻,三者给出相同的功率。
- $P = I^2 R$ 说明为什么大电流把导线加热得如此厉害。
Which is not · 不 a correct form of electric power for a resistor? · 哪一项不是电阻电功率的正确表达式？
The valid forms are $IV$, $I^2R$, $V^2/R$. $IR^2$ is wrong. · 有效形式包括$IV$、$I^2R$、$V^2/R$。$IR^2$是错误的。
Useful power and wasted heat
- In a resistor, all the power becomes heat — that is dissipation 耗散.
- In a motor, most becomes useful motion, with some lost to heat.
- Heaters and kettles are just resistors chosen to dissipate a lot.
- Thin wires with high current can overheat — a fire risk.
有用功率与浪费的热
- 在电阻中,所有功率都变成热——这就是耗散。
- 在电动机中,大部分变成有用的运动,一些损失为热。
- 加热器和水壶只是被选来大量耗散的电阻。
- 大电流的细导线可能过热——有起火风险。
Select all · 所有 true statements about electric power. · 选择关于电功率的所有正确陈述。
P = IV, resistor power heats, energy = P×t. Power (rate) ≠ energy (total). · P = IV，电阻功率产生热量，能量 = P×t。功率（速率）≠ 能量（总量）。
Paying for energy: the kilowatt-hour
- Your electricity bill charges for energy, not power.
- Energy $=$ power $\times$ time; one kilowatt-hour is $1\ \text{kW}$ for $1$ hour.
- A $2\ \text{kW}$ heater for $3$ hours uses $6\ \text{kWh}$.
- Power tells the rate; multiply by time to get the bill.
为能量付费:千瓦时
- 你的电费按能量收费,不是功率。
- 能量 $=$ 功率 $\times$ 时间;一千瓦时是 $1\ \text{kW}$ 用 $1$ 小时。
- 一个 $2\ \text{kW}$ 的加热器用 $3$ 小时消耗 $6\ \text{kWh}$。
- 功率告诉你速率;乘以时间得到账单。
Your electricity bill charges for energy (power × time), not for power itself. · 您的电费账单收取的是能量（功率×时间），而非功率本身。
Energy = power × time, billed in kilowatt-hours. · 能量 = 功率 × 时间，计费单位为千瓦时。
A bulb runs at $0.5\ \text{A}$ from a $230\ \text{V}$ supply. Find its power.
- $P = IV = 0.5 \times 230 = 115\ \text{W}$.
- It converts $115$ joules of energy every second.
一个灯泡在 $230\ \text{V}$ 电源下以 $0.5\ \text{A}$ 工作。求它的功率。
- $P = IV = 0.5 \times 230 = 115\ \text{W}$。
- 它每秒转换 $115$ 焦耳的能量。
Keep power (rate, in watts) separate from energy (total, in joules or kWh). Your bill is for energy $=$ power $\times$ time, not for power. A high-power device used briefly can cost less than a low-power one left on for days.
把功率(速率,单位瓦特)和能量(总量,单位焦耳或千瓦时)分开。你的账单是能量 $=$ 功率 $\times$ 时间,不是功率。一个高功率器件短暂使用可能比一个低功率器件开好几天更便宜。
Power is energy per second: $P = IV$ (watts), also $P = I^2R = V^2/R$ for a resistor. In a resistor it all becomes heat (dissipation). Energy $=$ power $\times$ time — billed as kilowatt-hours.
功率是每秒的能量:$P = IV$(瓦特),对电阻也有 $P = I^2R = V^2/R$。在电阻中它全变成热(耗散)。能量 $=$ 功率 $\times$ 时间——按千瓦时计费。