quickconverts.org
☰

Inductance In Parallel Formula

Image related to inductance-in-parallel-formula

Inductance in Parallel: A Comprehensive Guide



Inductance, a fundamental concept in electrical engineering, describes the ability of a conductor to store energy in a magnetic field when an electric current passes through it. When inductors are connected in parallel, their combined effect on the circuit differs significantly from inductors in series. Understanding how to calculate the total inductance of parallel inductors is crucial for circuit analysis and design. This article will explore the formula for calculating the total inductance of inductors connected in parallel, alongside practical examples and frequently asked questions.


1. Understanding Inductance and its Units



Before delving into parallel inductance calculations, let's revisit the concept of inductance itself. An inductor, often symbolized as 'L', is a passive electrical component that stores energy in a magnetic field. This magnetic field is generated when an electric current flows through the inductor's coil. The unit of inductance is the Henry (H), named after Joseph Henry, a pioneer in electromagnetism. One Henry is defined as the inductance that produces one volt across the inductor when the current through it changes at a rate of one ampere per second.


2. Inductors in Parallel: The Fundamental Formula



Unlike resistors in parallel, where the reciprocal of the total resistance equals the sum of the reciprocals of individual resistances, the formula for inductors in parallel is simpler. When inductors are connected in parallel, the total inductance (L<sub>T</sub>) is given by:

1/L<sub>T</sub> = 1/L<sub>1</sub> + 1/L<sub>2</sub> + 1/L<sub>3</sub> + ... + 1/L<sub>n</sub>

where L<sub>1</sub>, L<sub>2</sub>, L<sub>3</sub>, ..., L<sub>n</sub> are the individual inductances of the inductors connected in parallel. This formula is analogous to calculating the total capacitance of capacitors connected in series. The total inductance in a parallel arrangement is always less than the smallest individual inductance. This is because the parallel configuration provides multiple paths for the magnetic flux, reducing the overall inductance.


3. Calculating Total Inductance: Worked Examples



Let's illustrate the formula with some examples.

Example 1: Two inductors, L<sub>1</sub> = 10 H and L<sub>2</sub> = 20 H, are connected in parallel. What is the total inductance?

Using the formula:

1/L<sub>T</sub> = 1/10 H + 1/20 H = 3/20 H

Therefore, L<sub>T</sub> = 20/3 H ≈ 6.67 H. Notice that the total inductance (6.67 H) is less than the smallest individual inductance (10 H).

Example 2: Three inductors, L<sub>1</sub> = 5 H, L<sub>2</sub> = 10 H, and L<sub>3</sub> = 15 H, are connected in parallel. Calculate the total inductance.

1/L<sub>T</sub> = 1/5 H + 1/10 H + 1/15 H = (6 + 3 + 2)/30 H = 11/30 H

Therefore, L<sub>T</sub> = 30/11 H ≈ 2.73 H. Again, the total inductance is less than the smallest individual inductance.


4. Practical Applications and Considerations



The parallel inductance formula is essential in various applications. For instance, in filter design, parallel inductors are often used to create specific frequency responses. In power electronics, parallel inductors might be used to distribute current more evenly across multiple components, improving efficiency and reducing stress on individual components. However, it's crucial to consider the mutual inductance between inductors if they are physically close. Mutual inductance arises due to the magnetic fields of the inductors influencing each other. If mutual inductance is significant, the simple parallel inductance formula will be inaccurate, requiring a more complex analysis considering the mutual coupling coefficient. Similarly, the parasitic capacitance and resistance of the inductors can become significant at higher frequencies, altering the overall impedance and requiring more sophisticated models.


5. Summary



Calculating the total inductance of inductors connected in parallel is a crucial aspect of circuit analysis. The reciprocal of the total inductance is equal to the sum of the reciprocals of the individual inductances. The total inductance is always less than the smallest individual inductance. This formula is fundamental in various applications, including filter design and power electronics. However, the accuracy of this formula is affected by factors such as mutual inductance and parasitic effects, which should be considered in more complex scenarios.


6. Frequently Asked Questions (FAQs)



Q1: What happens if one inductor in a parallel combination is open-circuited?

A1: If one inductor is open-circuited, it effectively removes itself from the parallel combination. The total inductance becomes equal to the equivalent inductance of the remaining parallel inductors.

Q2: Can I use this formula for inductors with different tolerances?

A2: Yes, you can use the formula, but keep in mind that the calculated total inductance will also have a tolerance that depends on the tolerances of the individual inductors. The resulting tolerance will likely be larger than the tolerance of any single inductor.

Q3: How does mutual inductance affect the parallel inductance calculation?

A3: Mutual inductance between inductors complicates the calculation. The simple formula provided doesn't account for it. A more complex formula involving the mutual inductance coefficient is needed for accurate calculation.

Q4: What is the effect of parasitic resistance on the parallel inductance calculation?

A4: Parasitic resistance in the inductors introduces losses and affects the overall impedance, especially at higher frequencies. The simple formula ignores this resistance and is thus most accurate at lower frequencies.

Q5: How does the frequency of the applied signal affect the parallel inductance?

A5: At higher frequencies, parasitic capacitance and resistance within the inductors become more significant, causing deviations from the calculated low-frequency inductance. The simple formula is most accurate at low frequencies where these parasitic effects are negligible.

Links:

Converter Tool

Conversion Result:

=

Note: Conversion is based on the latest values and formulas.

Formatted Text:

b tan
55 kg to lbs
french ww1 machine guns
1 0009
2 5 10 8
historical villain upgrade
gannicus gladiator
blu ray rpm
how to stop port 8080
continuous view of development
rudimentary meaning
80 in inches
what is the chemical formula of citric acid
12 ft in cm
galore tube

Search Results:

什么是自感和互感 - 知乎 图片来自electric tutorial 如果两个线圈在一个共同的软铁芯整体耦合上紧紧缠绕在另一个之上，则据说它们之间存在任何因磁通泄漏引起的损失都将非常小。然后假设两个线圈之间存在完美的 …

电笔的“直接检测”和“感应断点检测”有什么区别?_百度知道 电笔的“直接检测”和“感应断点检测”有什么区别?直接检测是指直接接触金属导线测试电压有无。感应检测：1． 轻触感应、断点测量（INDUCTANCE）按键，测电笔金属前端靠近被检测物， …

电容 电感 电阻 二级管 它们的英文全称是什么呢?以及单位是什么 … 1 Mar 2011 · 电容： 英文名称：capacitance 用C表示，单位有F,常用的电容单位还有毫法 (mF)、微法 (μF)、纳法 (nF)和皮法 (pF) (皮法又称微微法)等 电感： 英文名称：inductance 用L表 …

第 6 章 互感耦合电路 - 知乎 17 Dec 2021 · 式中， L 1 和 L 2 分别为 N 1 和 N 2 的自电感（self⁃inductance）。 M 21 和 M 12 分别为 N 1 对 N 2 和 N 2 对 N 1 的互感（mutual inductance）。

请问既然电感的英语是“inductance”,为什么却简称为“l”呢？_百度知道 26 Oct 2024 · 答案： 电感的英文“inductance”简称为“L”，这是因为“L”是“inductance”的首字母，且在电子领域中，为了简便和统一，常常使用首字母或缩写来代表各种元件和概念。因此，电感 …

直流偏置下的电感值实例（inductance under DC bias） - 知乎 用这种方法可以测试出厂家是否替换了材料。大多数时候这个最终值都会有+、- 15%的偏差，所以即使很多生产厂家换了材料也很难测出，不过一般情况下，在电参数都满足要求的条件下，很 …

leakage inductance是什么意思，能不能详细解释是什么东西吗？ leakage inductance是什么意思，能不能详细解释是什么东西吗？漏电感 漏电感，或漏感，（英文:Leakage inductance）是变压器中一次绕线与二次绕线的耦合系数 [1]数值较小时，构成变压器 …

试电笔上面的按键写着DIRECTINDUCTANCE是什么意思_百度知道 12 Aug 2024 · 试电笔上面的按键写着DIRECTINDUCTANCE是什么意思试电笔上的按键“DIRECT”和“INDUCTANCE”分别代表了两种不同的测量模式，具体如下：1. **DIRECT（直接 …

试电笔上面的按键写着“DIRECT、INDUCTANCE”是什么意思？ INDUCTANCE（B键），感应测量按键（离液晶屏较近），也就是用批头感应接触线路时，请按此按钮。 含有这两种键的电笔一般称为数显测电笔。 使用A键时，为直接检测，最后数字为所 …

电感（inductance）对一个特定的线圈是一个固定值吗？ - 知乎 6 May 2020 · 电感（inductance）对一个特定的线圈是一个固定值吗？ 我一直觉得理想的电感和电容一样，是一个固定的物理量，不太会随输入信号的变化而改变。 但今天在用COMSOL仿真 …