If you're seeing this message, it means we're having trouble loading external resources on our website.

# 串联的电阻器

## 电阻串联

### 串联电阻的特性

• 三个电阻的电压必须加起来为${v}_{\text{S}}$
• 电流$i$流过所有三个电阻。

${v}_{\text{S}}={v}_{\text{R1}}+{v}_{R2}+{v}_{R3}$
${v}_{\text{R}1}=i\cdot {\text{R}}_{1}\phantom{\rule{2em}{0ex}}{v}_{\text{R}2}=i\cdot {\text{R}}_{2}\phantom{\rule{2em}{0ex}}{v}_{\text{R}3}=i\cdot {\text{R}}_{3}\phantom{\rule{2em}{0ex}}$

${v}_{\text{S}}=i\cdot \text{R1}\phantom{\rule{0.167em}{0ex}}+\phantom{\rule{0.167em}{0ex}}i\cdot \text{R2}\phantom{\rule{0.167em}{0ex}}+\phantom{\rule{0.167em}{0ex}}i\cdot \text{R3}$

${v}_{\text{S}}=i\phantom{\rule{0.167em}{0ex}}\phantom{\rule{0.167em}{0ex}}\left(\text{R1}+\text{R2}+\text{R3}\right)$

$i=\frac{{v}_{\text{S}}}{\left(\text{R1}+\text{R2}+\text{R3}\right)}$

### 等效串联电阻

${\text{R}}_{\text{series}}=\text{R1}+\text{R2}+\text{R3}$

${\text{R}}_{\text{series}}=\text{R1}+\text{R2}+\text{…}+{\text{R}}_{\text{N}}$

### 电压在串联的电阻之间的分配

${v}_{\text{R}1}=i\cdot {\text{R}}_{1}\phantom{\rule{2em}{0ex}}{v}_{\text{R}2}=i\cdot {\text{R}}_{2}\phantom{\rule{2em}{0ex}}{v}_{\text{R}3}=i\cdot {\text{R}}_{3}\phantom{\rule{2em}{0ex}}$

$\text{例题 1}$
a. 三个电阻的电流$i$和电压是多少?
b. 解释为何各个电阻的电压的和为 ${\text{V}}_{\text{S}}$

### 回顾

（电阻值）最大的电阻其电压最大还是最小？

（电阻值）最小的电阻其电压最大还是最小？

### 摘要

${\text{R}}_{\text{series}}=\text{R1}+\text{R2}+\text{…}+{\text{R}}_{\text{N}}$