# 並聯電路

## 電阻器

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

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

${\displaystyle i=i_{1}+i_{2}+\cdots +i_{n}={\frac {v}{R_{1}}}+{\frac {v}{R_{2}}}+\cdots +{\frac {v}{R_{n}}}}$

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

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

${\displaystyle G=1/R}$

${\displaystyle n}$個电阻器並聯的等效电導${\displaystyle G_{eq}}$

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

## 電容器

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

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

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

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

## 電感器

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

• 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「並聯互助」，以方程式表示，
${\displaystyle L_{eq}={\frac {L_{1}L_{2}-M^{2}}{L_{1}+L_{2}-2M}}}$
• 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「並聯互消」，以方程式表示，
${\displaystyle L_{eq}={\frac {L_{1}L_{2}-M^{2}}{L_{1}+L_{2}+2M}}}$

## 被動元件

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

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

${\displaystyle Z_{eq}=R_{eq}+jX_{eq}}$

${\displaystyle R_{eq}={\frac {(X_{1}R_{2}+X_{2}R_{1})(X_{1}+X_{2})+(R_{1}R_{2}-X_{1}X_{2})(R_{1}+R_{2})}{(R_{1}+R_{2})^{2}+(X_{1}+X_{2})^{2}}}}$
${\displaystyle X_{eq}={\frac {(X_{1}R_{2}+X_{2}R_{1})(R_{1}+R_{2})-(R_{1}R_{2}-X_{1}X_{2})(X_{1}+X_{2})}{(R_{1}+R_{2})^{2}+(X_{1}+X_{2})^{2}}}}$

## 雙埠網路

${\displaystyle n}$雙埠網路也可以以並聯方式連接在一起。

## 參考文獻

1. Alexander, Charles; Sadiku, Matthew, Fundamentals of Electric Circuits 3, revised, McGraw-Hill: pp. 35–36, 2006, ISBN 9780073301150
2. ^ Ghosh, Smarajit, Fundamentals of Electrical and Electronics Engineering, PHI Learning Pvt. Ltd.: pp. 113–117, 2004, ISBN 9788120323162
• 范瓦尔肯堡. 电学基础 (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