Compound DC Circuits · 复合直流电路
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| series/ˈsɪəriːz/ | 串联 | chuàn lián |
| parallel circuit/ˈpærəlel ˈsɜːkɪt/ | 并联 | bìng lián |
Fairy lights: one dead bulb, and the whole string goes out
- Old fairy lights were wired in a single line — one broken bulb killed them all.
- Modern ones keep glowing because they are wired a different way.
- The two ways to connect components are series 串联 and parallel circuit 并联.
- Which you choose changes the total resistance, the current, and what happens when one fails.
彩灯串:一个坏灯泡,整串就全灭
- 老式彩灯串是接成一条线的——一个坏灯泡就让它们全灭。
- 现代的仍然亮着,因为它们接线方式不同。
- 连接元件的两种方式是串联和并联。
- 你选哪一种,会改变总电阻、电流,以及某个元件失效时会发生什么。
Series: one single path
- In series, components sit in a single line, one after another.
- The same current flows through each, and the voltages add up to the supply voltage.
- Resistances add: $R_{\text{total}} = R_1 + R_2 + \cdots$.
- Break any one and the whole loop stops — like the old fairy lights.
串联:单一路径
- 在串联中,元件排成一条线,一个接一个。
- 相同的电流流过每一个,电压加起来等于电源电压。
- 电阻相加:$R_{\text{total}} = R_1 + R_2 + \cdots$。
- 断开任一个,整个回路就停——像老式彩灯串。
Two $6\ \Omega$ resistors are in series · 串联. What is the total resistance, in $\Omega$? · 两个$6\ \Omega$电阻串联。总电阻是多少，单位为$\Omega$？
Series resistances add: $6 + 6 = 12\ \Omega$. · 串联电阻相加：$6 + 6 = 12\ \Omega$。
In a series circuit, the current through each component is: · 在串联电路中，通过每个元件的电流是：
One path means the same current flows through every series component. · 一条路径意味着相同的电流流经每个串联元件。
Parallel: separate branches
- In parallel, components sit on separate branches across the same two points.
- Each branch has the same voltage, and the branch currents add to the total.
- The total resistance is less than any single branch: $\dfrac{1}{R_{\text{total}}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots$.
- Break one branch and the others keep working — like modern lights and home wiring.
并联:分开的支路
- 在并联中,元件位于跨接同两点的分开支路上。
- 每条支路有相同的电压,支路电流相加等于总电流。
- 总电阻小于任何单条支路:$\dfrac{1}{R_{\text{total}}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots$。
- 断开一条支路,其余的照常工作——像现代灯和家庭布线。
Series vs parallel · 串联与并联
Switch between series and parallel and see how the current through each bulb changes. · 切换串联和并联模式，观察通过每个灯泡的电流如何变化。
Two $6\ \Omega$ resistors are in parallel · 平行. What is the total resistance, in $\Omega$? · 两个$6\ \Omega$电阻并联。总电阻是多少，单位为$\Omega$？
$\tfrac1R = \tfrac16 + \tfrac16 = \tfrac26 \Rightarrow R = 3\ \Omega$.
Components in parallel all have the same ____ across them. · 并联的所有元件两端都有相同的____。
Parallel branches share the same two points, so the same voltage. · 并联支路共享相同的两个端点，因此具有相同的电压。
Select all · 所有 true statements about series and parallel circuits. · 选择所有关于串联和并联电路的正确陈述。
Series add; parallel give a smaller total; homes use parallel. Parallel resistances do not simply add. · 串联相加；并联得到更小的总电阻；家庭使用并联。并联电阻不会简单相加。
Why homes wire in parallel
- Household sockets are all in parallel, so each gets the full mains voltage.
- You can switch one appliance off without cutting power to the rest.
- Adding more parallel paths lowers the total resistance and draws more total current.
- That is why overloading a circuit (too many devices) can trip a breaker.
家里为何并联布线
- 家用插座全都并联,所以每个都得到完整的市电电压。
- 你可以关掉一个电器而不切断其余的电源。
- 增加更多并联路径会降低总电阻,并抽取更多总电流。
- 这就是为什么让电路过载(设备太多)会跳闸。
Adding a resistor in parallel makes the total resistance smaller. · 并联添加一个电阻会使总电阻变小。
Each parallel branch is an extra path, lowering the total resistance. · 每个并联支路都是一条额外的路径，降低了总电阻。
Adding resistors in parallel makes the total resistance smaller, not larger — a surprise for many students. Each new branch is an extra path for current, so more current flows overall even though you "added a resistor".
并联增加电阻会让总电阻变小,而非变大——这让许多学生意外。每条新支路都是电流的一条额外路径,所以即使你"加了一个电阻",总电流反而更大。
Two $6\ \Omega$ resistors are connected (a) in series, (b) in parallel. Find each total.
- Series: $R = 6 + 6 = 12\ \Omega$.
- Parallel: $\dfrac{1}{R} = \dfrac{1}{6} + \dfrac{1}{6} = \dfrac{2}{6}$, so $R = 3\ \Omega$.
两个 $6\ \Omega$ 的电阻(a)串联、(b)并联。求各自的总电阻。
- 串联:$R = 6 + 6 = 12\ \Omega$。
- 并联:$\dfrac{1}{R} = \dfrac{1}{6} + \dfrac{1}{6} = \dfrac{2}{6}$,所以 $R = 3\ \Omega$。
Series components share one path: currents equal, voltages add, resistances add ($R = R_1+R_2$). Parallel components share two points: voltages equal, currents add, and the total resistance is smaller than any branch ($\tfrac1R = \tfrac1{R_1}+\tfrac1{R_2}$). Homes wire in parallel.
串联元件共享一条路径:电流相同、电压相加、电阻相加($R = R_1+R_2$)。并联元件共享两点:电压相同、电流相加,总电阻小于任何支路($\tfrac1R = \tfrac1{R_1}+\tfrac1{R_2}$)。家里并联布线。