91Ó°ÊÓ

Magnetic or electromagnetic induction is the process of producing an electromotive force across an electrical conductor in a shifting magnetic field. Michael Faraday discovered induction in\({\rm{1831}}\), which James Clerk Maxwell formally defined as Faraday's law of induction.

For coils, the reactive resistance is evaluated using the formula:

\({X_L}{\rm{ }} = {\rm{ }}2\pi fL\)

\(L{\rm{ }} = {\rm{ }}\frac{{{X_L}}}{{2\pi f}}\)

We put the numerical values and then obtain:

\(\begin{aligned} L{\rm{ }} &= {\rm{ }}\frac{{2000}}{{2\pi {\rm{ }} \times {\rm{ }}15000}}\\ &= {\rm{ }}21.2{\rm{ }}mH\end{aligned}\)

Therefore, the minimum inductance is: \(21.2{\rm{ }}mH\).

\(\begin{aligned} {X_L}{\rm{ }} &= {\rm{ }}2\pi {\rm{ }} \times {\rm{ }}60{\rm{ }} \times {\rm{ }}0.0212\\ &= {\rm{ }}8{\rm{ }}\Omega \end{aligned}\)

Therefore, the reactance is: \(8{\rm{ }}\Omega \).