# 串聯電路

## 電阻器

${\displaystyle v_{k}=i_{k}R_{k}=iR_{k}}$

${\displaystyle i=i_{1}=i_{2}=\cdots =i_{n}}$

${\displaystyle v=v_{1}+v_{2}+\cdots +v_{n}=i(R_{1}+R_{2}+\cdots +R_{n})}$

${\displaystyle R_{eq}=R_{1}+R_{2}+\cdots +R_{n}}$

${\displaystyle v=iR_{eq}}$

${\displaystyle {\frac {v_{k1}}{v_{k2}}}={\frac {R_{k1}}{R_{k2}}}}$

${\displaystyle G=1/R}$

${\displaystyle n}$個電阻器串聯的等效電導${\displaystyle G_{eq}}$

${\displaystyle {\frac {1}{G_{eq}}}={\frac {1}{G_{1}}}+{\frac {1}{G_{2}}}+\cdots +{\frac {1}{G_{n}}}}$

${\displaystyle G_{eq}={\frac {G_{1}G_{2}}{G_{1}+G_{2}}}}$

## 電容器

${\displaystyle i_{k}=C_{k}{\frac {\mathrm {d} v_{k}}{\mathrm {d} t}}}$

${\displaystyle i=i_{1}=i_{2}=\cdots =i_{n}}$

${\displaystyle v=v_{1}+v_{2}+\cdots +v_{n}}$

${\displaystyle {\frac {\mathrm {d} v}{\mathrm {d} t}}={\frac {\mathrm {d} v_{1}}{\mathrm {d} t}}+{\frac {\mathrm {d} v_{2}}{\mathrm {d} t}}+\cdots +{\frac {\mathrm {d} v_{n}}{\mathrm {d} t}}={\frac {i}{C_{1}}}+{\frac {i}{C_{2}}}+\cdots +{\frac {i}{C_{n}}}}$

${\displaystyle {\frac {1}{C_{eq}}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+\cdots +{\frac {1}{C_{n}}}}$

## 電感器

${\displaystyle L_{eq}=L_{1}+L_{2}+\cdots +L_{n}}$

• 假設兩個電感器分別產生的磁場或磁通量，其方向相同，則稱為「串聯互助」，以方程式表示，
${\displaystyle L_{eq}=L_{1}+L_{2}+2M}$
• 假設兩個電感器分別產生的磁場或磁通量，其方向相反，則稱為「串聯互消」，以方程式表示，
${\displaystyle L_{eq}=L_{1}+L_{2}-2M}$

${\displaystyle L_{eq}=(M_{11}+M_{22}+M_{33})+(M_{12}+M_{13}+M_{23})+(M_{21}+M_{31}+M_{32})}$

${\displaystyle L_{eq}=(M_{11}+M_{22}+M_{33})+2(M_{12}+M_{13}+M_{23})}$

## 被動元件

${\displaystyle Z_{eq}=\ Z_{1}+Z_{2}+\cdots +Z_{n}}$

${\displaystyle Z_{eq}=R_{eq}+jX_{eq}=(R_{1}+R_{2}+\cdots +R_{n})+j(X_{1}+X_{2}+\cdots +X_{n})}$

## 雙埠網路

${\displaystyle n}$雙埠網路也可以以串聯方式連接在一起。

## 參考文獻

1. Alexander, Charles; Sadiku, Matthew, Fundamentals of Electric Circuits 3, revised, McGraw-Hill: pp. 35–36, 2006, ISBN 9780073301150
2. ^ Williams, Tim, The Circuit Designer's Companion, Butterworth-Heineman: pp.96–97, 2005, ISBN 0750663707
• 范瓦爾肯堡. 電學基礎 (M). 高等教育出版社. ISBN 978-7-04-000794-7.
• Smith, R.J. (1966), Circuits, Devices and Systems, Wiley International Edition, New York. Library of Congress Catalog Card No. 66-17612