Question

At what frequency will a\(30.0\,{\rm{mH}}\)inductor have a reactance of\(100\,{\rm{\Omega }}\)?

Short answer

The frequency is, \(530.52\,{\rm{Hz}}\).

Step-by-step solution

Identification of the given data

The given data can be listed below as,

• The inductor resistance is,\({X_L} = 100\,{\rm{\Omega }}\).
• The inductor inductance is, \(L = 30.0\,{\rm{mH}}\).

Define Electromagnetic Induction

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.

Evaluating the inductive resistance

The inductive resistance is evaluated using the formula as:

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

In the other parameters, we solve for the frequency, thus evaluating:

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

Substitute all the value in the above equation.

\(\begin{aligned} f{\rm{ }} &= {\rm{ }}\frac{{100\,{\rm{\Omega }}}}{{2\pi {\rm{ }} \times {\rm{ }}0.03\,{\rm{H}}}}\\ &= {\rm{ }}530.52\,{\rm{Hz}}\end{aligned}\)

Therefore, the frequency is, \(530.52\,{\rm{Hz}}\).