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Inductance formula
The term inductance was invented by Oliver Heaviside in 1886. Inductance is the property of a conductor to resist changes in the electrical current passing through it.
The electric current generates a magnetic field around a conductor. The strength of the field is proportional to the magnitude of the current and is not affected by the fluctuations in the current.
Faraday’s law of induction states that any change in the magnetic field generates an electromagnetic force in the conductors. This process is called electromagnetic induction.
Inductance is found in many electrical and electronic systems. The gears have a variety of names. Some examples of inductors include coils, chokes, and transformers.
The SI unit used for inductance is Henry (H). It can be used to express the current and voltage rate of change.
Inductance Formula
L = μN²A/l
‘L’ stands for Inductance (H)
‘μ’ stands for permeability (Wb/Am)
‘N’ stands for the number of turns taken by the coil
‘A’ stands for the circumference of the coil
‘l’ stands for the length of the coil (m)
Derivation Of The Inductance Formula
E = N ( dΦ / dt )
N is the number of turns taken by the coil and E is the induced EMF of the coil.
Using Lenz’s law
E = (-N) × (dΦ/dt)
To calculate the value of inductance
E = (-L) × (di/dt)
N = dΦ = L di
B = Flux density
A = Coil area
Li = NΦ = NBA
Hl = Ni
‘H’ denotes the magnetising force of the magnetic flux.
B = μΗ
Li = NBA
L = NBA/i = N²BA/Ni
N²BA/Hl = N²μHA/Hl
therefore,
L = μN²A/l
Voltage in a coil can be calculated as:
V = L × di/dt
‘V’ stands for voltage
‘L’ is the value of inductance
‘i’ is used to denote current
‘t’ is the time taken
To calculate inductance reactance:
X= 2πfL
‘X’ is the reactance
‘f’ is the frequency
‘L’ is the inductance
Inductance in series is calculated as:
L = L₁+ L₂ + L₃…. + Lₙ
Parallel inductance can be calculated as-
1/L = 1/L₁ + 1/L₂ + 1/L₃…. + 1/Lₙ
Solved Example
Question- Calculate the corresponding resistance when 16H, 10H, and 21H inductors are joined in a series.
Answer- L₁ = 16 H
L₂ = 10 H
L₃ = 21 H
L = L₁ + L₂ + L₃
L = 16 + 10 + 21
= 47 H
