Inductance Formula

We are aware that whenever an electric current flows through a conductor, a magnetic field surrounding it is produced. A varying current results in a varying magnetic field. Due to this, the magnetic flux varies and an electromotive force is induced. The inductance value is represented as L and its unit is Henry. One Henry value is equivalent to the induced one volt by changing of current in one ampere per second in an inductance value. The inductance value is of two types. One is the mutual inductance and another one is self-inductance.

Formula for Inductance

\(L=\mu N^2A/l\)

Where
L = inductance in Henry (H)
μ = permeability (Wb/A.m)
N = number of turns in the coil
A = area encircled by the coil
l = length of the coil(m)

The voltage induced in a coil, (V) with an inductance of L is given by

\(V=L\frac{di}{dt}\)

Where,
V = voltage(volts)
L = inductance value (H)
I = the current is (A)
t = time taken (s)

The reactance of inductance is given by

\(X=2\pi fL\)

Where,
Reactance is X in ohm (Ω)
the frequency is f in Hz,
Inductance is L in Henry (H)

The total series inductance is

\(L=L_1+L_2+L_3+….+L_n\)

The parallel inductance is
\(\frac{1}{L}=\frac{1}{L_1}+\frac{1}{L_2}+\frac{1}{L_3}+….+\frac{1}{L_n}\)

Where, L1, L2, L3….. Ln  are the inductance values.

Inductance – Solved Examples

Problem 1: Compute the equivalent resistance if inductors of 5H, 2H and 7 H are linked in series?
Answer:

Known: L1 = 5H, L2 = 2H, L3 = 7H
The series inductance is articulated as
L = L1 + L+ L3
= 5H + 2H + 7H  = 14 H

Question 2: An inductor of 50 H is linked to a circuit and a frequency of 200 Hz is provided. Compute the reactance?
Solution:

Known:

Reactance X= ?,

frequency f = 200 Hz,

inductance L = 50 Henry
The reactance is articulated as
X = 2 π f L
= 2 × 3.14× 200 × 50
X= 12560 Ω

 

1 Comment

  1. How to calculate inductance

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