Question

What value of inductance should be used if a\(20.0\,{\rm{k\Omega }}\)reactance is needed at a frequency of\(500\,{\rm{Hz}}\)?

Short answer

The Inductive resistance is obtained as: \(6.37\,{\rm{H}}\).

Step-by-step solution

Identification of the given data

The given data can be listed below as,

• The inductor resistance is,\({X_L} = 20.0\,{\rm{k\Omega }}\).
• The frequency is, \(f = 500\,{\rm{Hz}}\).

Definition of inductance

When comparing the amount of the electromotive force, or voltage, produced in a conductor (typically in the form of a coil), to the rate of change of the electric current that generates the voltage, inductance, a feature of the conductor, is measured.

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 inductive resistance, thus evaluating:

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

Substitute all the value in the above equation.

\(\begin{aligned} L &= \frac{{2 \times {{10}^4}\,{\rm{\Omega }}}}{{2\pi \times 500\,{\rm{Hz}}}}\\ &= 6.37\,{\rm{H}}\end{aligned}\)

Therefore, the Inductive resistance is, \(6.37\,{\rm{H}}\).