电感公式
电感是每个物理系学生都应该熟悉的术语。它有自己的公式，经常与电阻和电容结合使用。 Oliver Heaviside 在 1886 年首次创造了这个短语。此外，我们使用 L 来表示电路图上的电感器和方程式中的电感器，以纪念杰出的物理学家 Heinrich。让我们了解一下电感器公式以及如何使用它来确定电感器任何项目。
电感
电感是电导体的一种特性，它可以抵抗通过它的电流的变化。电流的流动在导体周围产生磁场。场强与电流大小成正比，不受电流波动的影响。根据法拉第感应定律，磁场通过电路的任何变化都会在导体中产生电动势 (EMF)（电压），这一过程称为电磁感应。
电感可以在许多电气和电子系统以及电路中找到。这些齿轮有多种形状和尺寸，以及各种名称。示例包括线圈、扼流圈、变压器、电感器和其他部件。
电感的国际单位制单位是亨利（H） ，可以用电流和电压的变化率来表示。
电感公式
- 以下是电感公式，
L = μN2A/l
Where,
- L = Inductance (H),
- μ = Permeability (Wb/Am),
- N = The coil’s number of turns,
- A = The coil’s circumference,
- l = Length of coil (m).
推导
Given:
E = N(dϕ/dt)
The number of turns in the coil is N, and the induced EMF across the coil is E.
Using Lenz’s law, rewrite the above equation,
E = -N(dϕ/dt)
The previous equation is modified to compute the value of inductance.
E = -N(dϕ/dt)
∴ E = -L(di/dt)
N = dΦ = L di
NΦ = Li
Hence,
The flux density is denoted by B, and the coil area is denoted by A.
Li = NΦ = NBA
Hl = Ni
The magnetizing force of the magnetic flux is denoted by H.
B = μH
Li = NBA
L = NBA/i = N2BA/Ni
N2BA/Hl = N2μHA/Hl
∴ L = μN2A/l
- 电感为 L 时，线圈中感应的电压 (V) 等于，
V = L × (di/dt)
Where,
- V = Voltage (volts),
- L = Value of Inductance (H),
- i = Current (A),
- t = Time taken (s).
- 电感电抗计算如下，
X = 2πfL
Where,
- X = Reactance (ohm),
- f = frequency (Hz),
- L = Inductance (H).
- 如果电感串联
L = L1 + L2 + L3 . . . . + Ln
- 如果电感并联
1/L = 1/L1 + 1/L2 + 1/L3 . . . . + 1/Ln
示例问题
问题 1：定义电感。
答案：
Inductance is a property of an electrical conductor that causes it to resist changes in the electric current passing through it. Since inductane has N in the formula, it means that the number of turns in the conductor are directly proportional to the inductance present. However, an interesting fact is that even straight conductors carry inductance just very little in amount to be considerable.
问题2：电感的SI单位是什么？
回答：
SI unit of Inductance is the henry (H). The discovery of inductance is credited to Faraday, however, the introduction of self inductance for a single circuit was first introduced by Henry. Therefore, the unit of inductance is dedicated to the scientist’s name.
问题 3：确定横截面积为 17 cm 2 、长度为 66.2 cm 的 210 匝螺线管的自感。
解决方案：
Given: μ = 4π × 10-7, N = 210 turns, A = 17 × 10-4, l = 66.2 × 10-2
Since,
L = μN2A/l
∴ L = ((4π × 10-7) × (210)2 × (17 × 10-4))/(66.2 × 10-2)
∴ L = 0.0001422
∴ L = 14.22 × 10-5 H
问题4：16H、10H、21H电感串联时对应的阻值是多少？
解决方案：
Given: L1 = 16 H, L2 = 10 H, L3 = 21 H
Since,
L = L1 + L2 + L3
∴ L = 16 + 10 + 21
∴ L = 47 H
问题5：电路接一个61H的电感，提供240Hz的频率。计算电抗？
解决方案：
Given: f = 240 Hz, L = 61 H
Since,
X = 2πfL
∴ X = 2 × 3.14 × 240 × 61
∴ X = 91939 ohm
问题6：26H、16H、21H、30H电感并联时对应的阻值是多少？
解决方案：
Given: L1 = 26 H, L2 = 16 H, L3 = 21 H, L4 = 30 H
Since,
1/L = 1/L1 + 1/L2 + 1/L3 + 1/L4
∴ 1/L = 1/26 + 1/16 + 1/21 + 1/30
∴ 1/L = 0.03 + 0.06 + 0.04 + 0.03
∴ 1/L = 0.16 H
∴ L = 6.25 H