Demonstrative Video
Ampere-turns Calculations
In a magnetic circuit, flux produced, \[\phi=\frac{\text { m.m.f. }}{\text { reluctance }}=\frac{N I}{l / a \mu_{0} \mu_{r}}\] or \[\text { AT required, } N I=\frac{\phi l}{a \mu_{0} \mu_{r}}=\frac{B}{\mu_{0} \mu_{r}} l=H l\]
Series Magnetic Circuits
In series magnetic circuit without air-gap \(NI=\Phi\Re=Hl\)
It is a series circuit so same flux (\(\Phi\)) flows through the two medium- iron and air
Total reluctance \(\Re = \Re_{iron} + \Re_{air}\)
Since value of permeabilities are different for iron and air, the corresponding values of \(H\) too will be different \[\begin{aligned} H_{i} & =\dfrac{B}{\mu_{0}\mu_{i}}\\ H_{g} & =\dfrac{B}{\mu_{0}}\\ \therefore\Phi & =\dfrac{NI}{\left(\Re_{i}+\Re_{g}\right)} \end{aligned}\]
Series-Parallel magnetic circuit
\[\begin{aligned} \Phi & =\Phi_{1}+\Phi_{2}\\ NI & =Hl+H_{1}l_{1}+H_{g}l_{g}=\Re\Phi+\left(\Re_{1}+\Re_{g}\right)\Phi_{1}\\ \left(\Re_{1}+\Re_{g}\right)\Phi_{1} & =\Re_{2}\Phi_{2}\\ H_{1}l_{1}+H_{g}l_{g} & =H_{2}l_{2}\\ NI & =Hl+H_{2}l_{2} \end{aligned}\]