Compound Direct Current Circuits · 串并联混合电路
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| series/ˈsɪəriːz/ | 串联 | chuàn lián |
| parallel/ˈpærəlel/ | 并联 | bìng lián |
| equivalent resistance/ɪˈkwɪvələnt rɪˈzɪstəns/ | 等效电阻 | děng xiào diàn zǔ |
One bulb dies — does the whole string go dark?
- Old fairy lights: one bulb fails and the entire string goes out.
- Newer ones: a bulb fails but the rest stay lit.
- The difference is series 串联 versus parallel 并联 wiring.
- Real circuits mix both, so we need rules to combine resistors.
一个灯泡坏了——整串都会熄灭吗?
- 老式彩灯:一个灯泡坏了,整串都灭。
- 新式的:一个灯泡坏了,其余的照亮。
- 区别在于串联还是并联接线。
- 真实电路两者混合,所以我们需要合并电阻的规则。
Series: resistances add
- In series, components sit one after another on a single path.
- The same current flows through each; their voltages add up.
- The total resistance is just the sum: $R = R_1 + R_2 + \cdots$.
- Adding a series resistor always increases the total resistance.
串联:电阻相加
- 在串联中,元件在单一路径上一个接一个。
- 相同的电流流过每一个;它们的电压相加。
- 总电阻就是它们之和:$R = R_1 + R_2 + \cdots$。
- 加一个串联电阻总会增大总电阻。
Two resistors in series have a total resistance of: · 两个电阻串联的总电阻为：
Series resistances add: $R = R_1 + R_2$. · 串联电阻相加：$R = R_1 + R_2$。
In a series circuit, what is the same through every component? · 在串联电路中，每个元件上相同的是什么？
Series shares one current; voltages add. · 串联电路共享一个电流；电压相加。
Parallel: reciprocals add
- In parallel, components share the same two ends.
- Each gets the same voltage; their currents add up.
- The reciprocals add: $\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots$.
- The total is smaller than any single branch — more paths, less resistance.
并联:倒数相加
- 在并联中,元件共享相同的两端。
- 每一个得到相同电压;它们的电流相加。
- 倒数相加:$\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots$。
- 总值比任何单个支路都小——路径越多,电阻越小。
Series vs parallel · 串联与并联
Wire bulbs in parallel and compare the current and brightness with a series wiring. · 将灯泡并联连接，并与串联布线比较电流和亮度。
Two $4\ \Omega$ resistors in parallel give what total resistance (in Ω)? · 两个$4\ \Omega$电阻并联后的总电阻是多少（单位为Ω）？
$1/R = 1/4 + 1/4 = 1/2$, so $R = 2\ \Omega$. · $1/R = 1/4 + 1/4 = 1/2$，所以 $R = 2\ \Omega$。
The total resistance of a parallel combination is smaller than any single branch. · 并联组合的总电阻小于任何单个支路。
More paths for current means less total resistance. · 更多的电流路径意味着更小的总电阻。
Reduce a network step by step
- Find any pure series or pure parallel group and replace it with one resistor.
- Repeat, shrinking the circuit until a single resistor remains.
- That final value is the equivalent resistance 等效电阻.
- Then use $V = IR$ to find the total current from the battery.
一步步化简网络
- 找出任何纯串联或纯并联的组,用一个电阻替换它。
- 重复,把电路缩小到只剩一个电阻。
- 那个最终值就是等效电阻。
- 然后用 $V = IR$ 求出电池的总电流。
The single resistor that replaces a whole network is its ____ resistance. · 替代整个网络的单个电阻称为其____电阻。
That value is the equivalent resistance. · 该值即为等效电阻。
What each wiring means
- Series: one break kills the whole loop (old fairy lights).
- Parallel: each branch is independent (house wiring, new lights).
- Parallel also draws more total current — every branch adds its own.
- Homes use parallel so one switch doesn't turn off everything.
每种接线意味着什么
- 串联:一个断口毁掉整个回路(老式彩灯)。
- 并联:每条支路独立(家庭布线、新式彩灯)。
- 并联还取用更多总电流——每条支路加上自己的。
- 家庭用并联,这样一个开关不会关掉一切。
Select all · 所有 true statements about series and parallel. · 选择关于串联和并联的所有正确陈述。
Series adds, parallel adds reciprocals, and they share current/voltage respectively. Parallel is NOT a sum. · 串联相加，并联加倒数，并分别共享电流/电压。并联不是简单的加法求和。
Two $6\ \Omega$ resistors: find the total in series, then in parallel.
- 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 $6\ \Omega$ 电阻:求串联的总值,再求并联的。
- 串联:$R = 6 + 6 = 12\ \Omega$。
- 并联:$\dfrac{1}{R} = \dfrac{1}{6} + \dfrac{1}{6} = \dfrac{2}{6}$,所以 $R = 3\ \Omega$。
Parallel resistance is not the sum. Add the reciprocals, then flip: the total is always less than the smallest branch. Writing $R = R_1 + R_2$ for parallel is the most common circuit error.
并联电阻不是求和。把倒数相加,再翻转:总值总是小于最小的支路。把并联写成 $R = R_1 + R_2$ 是最常见的电路错误。
In series, resistances add ($R = R_1 + R_2$) and share the current; in parallel, reciprocals add ($1/R = 1/R_1 + 1/R_2$) and share the voltage, giving a smaller total. Reduce a network step by step to its equivalent resistance.
在串联中,电阻相加($R = R_1 + R_2$)并共享电流;在并联中,倒数相加($1/R = 1/R_1 + 1/R_2$)并共享电压,给出更小的总值。一步步把网络化简成它的等效电阻。