Question

Reluctance of a magnetic circuit is given by:
1. \(\frac{{{\mu _0}{\mu _r}A}}{l}\)
2. \(\frac{A}{{{\mu _0}{\mu _r}l}}\)
3. \(\frac{{{l^2}}}{{{\mu _0}{\mu _r}A}}\)
4. \(\frac{l}{{{\mu _0}{\mu _r}A}}\)

Answer 1

Correct Answer - Option 4 : \(\frac{l}{{{\mu _0}{\mu _r}A}}\)

Reluctance opposes the passage of magnetic flux lines. Reluctance is analogous to resistance.

We can define the reluctance as,

\(\Re = \frac{{mmf}}{{flux}}\)

We know that, \(H = \frac{{NI}}{l}\)

Where H is field strength

N is the number of turns in a coil

l is mean length of flux in a magnetic circuit

I is current through the coil

The flux in a magnetic circuit is given by

\(\phi = BA\)

\(= \mu HA\)

\(= \mu \left( {\frac{{NI}}{l}} \right)A\)

\(\Rightarrow \phi = \frac{{NI}}{{\frac{1}{\mu }\frac{l}{A}}} = \frac{{mmf}}{{reluctance}} = \frac{{mmf}}{\Re}\)

Now, we can define reluctance as \(\Re = \frac{l}{{\mu A}} = \frac{l}{{{\mu _0}{\mu _r}}A}\)