Question

A\(20.0\,{\rm{kHz}},{\rm{ }}16.0\,{\rm{V}}\)source connected to an inductor produces a\(2.00\,{\rm{A}}\)current. What is the inductance?

Short answer

The inductance is obtained as, \(63.7\,{\rm{\mu H}}\).

Step-by-step solution

Identification of the given data

The given data can be listed below as,

• The frequency is,\(f = 20.0\,{\rm{kHz}}\).
• The voltage is,\(U = 16.0\,{\rm{V}}\).
• The current is, \(I = 2.00\,{\rm{A}}\).

Evaluating the formula

The inductive reactance is evaluated using the formula:

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

Knowing the reactance, we can then simply apply the Ohm's law and get:

\(\begin{aligned} I &= \frac{U}{{{X_L}}}\\ &= \frac{U}{{2\pi fL}}\end{aligned}\)

Now solving to obtain the inductance as:

\(L = \frac{U}{{2\pi If}}\) ...(1)

Evaluating the inductance

The numerical values of inductance and we obtain:

Substitute all the value in the equation (1)

\(\begin{aligned} L &= \frac{{16.0\,{\rm{V}}}}{{2\pi \times 2.0\,{\rm{A}} \times 20000\,{\rm{Hz}}}}\\ &= 6.37 \times {10^{ - 5}}\,{\rm{H}}\\ &= 63.7\,{\rm{\mu H}}\end{aligned}\)

Therefore, the inductance is, \(63.7\,{\rm{\mu H}}\).