What is Reluctance?

Magnetic reluctance is defined as the opposition offered by a magnetic circuit to the production of magnetic flux. Magnetic reluctance is the property of the material that opposes the creation of magnetic flux in a magnetic circuit.

Magnetic reluctance also known as reluctance, magnetic resistance, or a magnetic insulator.

Reluctance of Transformer
Reluctance of Transformer Core

In an electrical circuit, the resistance opposes the flow of current in the circuit and it dissipates the electric energy. The magnetic the magnetic reluctance is similar to the resistance of an electrical circuit as it withstands the production of magnetic fluctuations in the magnetic circuit but does not provide a cause for the dispersion of energy instead it retains the magnetic field.

Reluctance is directly related to the length of the magnetic field and measures against the location of the cross section of the magnetic path.

It is a scalar quantity and denoted by S. Note that a scalar quantity is one which is fully described by a magnitude (or numerical value) only. No direction is required to define the scalar quantity.

Reluctance of Magnetic Bar

Reluctance of Magnetic Bar

Mathematically it can be expressed as

\begin{align*} S = \frac {l}{\mu_0 \mu_r A} \end{align*}

where, l = length of the magnetic path in meters

\mu_0 = permeability of free space (vacuum) = 4 \pi * 10^-^7 Henry/meter

\mu_r = relative permeability of a magnetic material

A = Cross sectional area in square meters (m^2)

In AC as well as DC magnetic fields, the reluctance is the ratio of the magnetomotive force (m.m.f) to the magnetic flux in a magnetic circuit. In a pulsating AC or DC field, the reluctance is also pulsating.

Thus it can be expressed as

\begin{align*} Relectance (S) = \frac {m.m.f}{flux} =  \frac {F}{\phi} \end{align*}

Reluctance in a Series Magnetic Circuit

Like in a series electrical circuit, the total resistance is equal to the sum of the individual resistances,

\begin{align*} R = R_1 + R_2 + R_3 +.............+R_n \end{align*}

Where, R = \frac {\rho l}{A}   (\rho = Resistivity)

Similarly, in a series of magnetic circuits, the total reluctance equals the sum of the individual reluctances encountered around the closed flux path.

\begin{align*} S = S_1 + S_2 + S_3 +.............+S_n \end{align*}

Where, S = \frac {l}{\mu_0 \mu_r A}

Reluctance Units

The unit of reluctance is ampere-turns per Weber (AT/Wb) or 1/Henry or H-1.

Reluctance Formula

(1) \begin{equation*} S = \frac {l}{\mu_0 \mu_r A} \end{equation*}

Where, \mu = \mu_0 \mu_r (In an electrical circuit \epsilon = \epsilon_0 \epsilon_r)

Therefore, S = \frac {l}{\mu A}

Where, \mu = permeability of the magnetic material

\begin{align*} Reluctance (S) = \frac {m.m.f}{flux} \end{align*}

(2) \begin{equation*} S = \frac {NI}{\phi} \end{equation*}

Comparing Equation (1) and (2), we get

\begin{align*}  \frac {l}{\mu_0 \mu_r A} = \frac {NI}{\phi} \end{align*}

Rearranging terms, we get

(3) \begin{equation*}  \frac {\phi}{\mu_0 \mu_r A} = \frac {NI}{l} \end{equation*}

But \frac {\phi}{A} = B and \frac {NI}{l} = H

put this into equation (3) we get,

\begin{align*}  \frac {B}{\mu_0} = H \end{align*}
\begin{align*} B = \mu_0 \mu_r H = \mu H \ (where, \mu = \mu_0 \mu_r) \end{align*}

Applications of Reluctance

  • In the transformer, reluctance used to reduce the effect of magnetic saturation. Fixed wind gaps in the transformer increase circuit suspicion and thus retain additional magnetic strength before filling the space.
  • Reluctance motor used for many speed applications such as the clock timer, signature devices, recording tools, etc., which is works on the principle of variable reluctance.
  • One of the main characteristics of the magnetically hard materials is that it has a strong magnetic reluctance which is used to create permanent magnets. Example: Tungsten steel, cobalt steel, chromium steel, alnico, etc….
  • The speaker magnet is covered with a soft magnetic material such as soft iron to minimize the effect of the stray magnetic field.
  • Multimedia loudspeakers are magnetically shielded in order to reduce magnetic interference caused to TV (televisions) and CRTs (Cathode Ray Tube).

Source: electrical4u.com

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