Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版:英文原文完整保留,中文紧随对应单元;术语采用 v20260916 确认表,自动语义审校结果可追溯。

Impedance

阻抗

While Ohm's Law applies directly to resistors in DC or in AC circuits, the form of the current-voltage relationship in AC circuits in general is modified to the form:

尽管欧姆定律直接适用于直流电路或交流电路中的电阻,但交流电路中电流-电压关系的形式通常会有所修改,形式为:

where I and V are the rms or "effective" values. The quantity Z is called impedance. For a pure resistor, Z = R. Because the phase affects the impedance and because the contributions of capacitors and inductors differ in phase from resistive components by 90 degrees, a process like vector addition (phasors) is used to develop expressions for impedance. More general is the complex impedance method.

其中I和V是均方根值或“有效值”。量Z称为阻抗。对于纯电阻,Z = R。由于相位影响阻抗,并且电容器和电感器的贡献与电阻元件在相位上相差90度,因此使用类似矢量加法(相量)的过程来发展阻抗的表达式。更一般的是复数阻抗方法。

Series and parallel combination of any two impedances
任意两个阻抗的串联和并联组合
Index

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Impedance Combinations

阻抗组合

Combining impedances has similarities to the combining of resistors, but the phase relationships make it practically necessary to use the complex impedance method for carrying out the operations. Combining series impedances is straightforward:

将阻抗组合与电阻的组合有相似之处,但相位关系使得实际操作中必须使用复数阻抗方法来进行运算。将串联阻抗组合起来是直接的:
Calculation
计算

Combining parallel impedances is more difficult and shows the power of the complex impedance approach. The expressions must be rationalized and are lengthy algebraic forms.

将并联阻抗结合起来更为困难,这展示了复阻抗方法的优势。这些表达式必须进行有理化处理,且形式为复杂的代数表达式。
Expressions
表达式
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Parallel Impedance Expressions

并联阻抗表达式

The complex impedance of the parallel circuit takes the form

并联电路的复阻抗形式为

when rationalized, and the components have the form

当有理化时,其分量形式为
Calculation
计算
Index

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Impedance Calculation

阻抗计算

Impedances may be combined using the complex impedance method.

阻抗可以用复阻抗方法进行组合。
For
Z1 = + j
对于 Z 1 = +j
中文译文中的待填/计算数值依次对应:1:z1r 2:z1x。实际数值以上方原输入框为准。
Z2 = + j

the series combination is

串联组合是
Zeq = + j= at phase.
Z_eq = +j = 在相位中。
中文译文中的待填/计算数值依次对应:1:zer 2:zex 3:zea 4:zep。实际数值以上方原输入框为准。

The parallel combination is

并联组合是
Zeq = + j= at phase.
Z_eq = +j = 在相位中。
中文译文中的待填/计算数值依次对应:1:zerp 2:zexp 3:zeap 4:zepp。实际数值以上方原输入框为准。

The units for all quantities are ohms. A negative phase angle implies that the impedance is capacitive, and a positive phase angle implies net inductive behavior.

所有量的单位都是欧姆。负的相位角表示阻抗是电容性的,正的相位角表示有净的电感性行为。
Parallel impedance expressions
并联阻抗表达式
Inductive reactance
感抗
Capacitive reactance
容抗
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计算模块中未附着于文字的输入框:
中文译文中的待填/计算数值依次对应:1:z2r 2:z2x。实际数值以上方原输入框为准。