For the A.C circuit as shown below, if the rms voltage across the resistor is 120 V. What is the value of the inductor?

We have RMS value of source

\({{\rm{V}}_{{\rm{RMS}}}} = \frac{{{{\rm{V}}_{\rm{m}}}}}{{\sqrt 2 }} = 150\)

Then, \({{\rm{V}}_{\rm{L}}} = \sqrt {{\rm{V}}_{{\rm{RMS}}}^2 - {\rm{V}}_{\rm{R}}^2} = \sqrt {{{150}^2} - {{120}^2}}\)

\(\Rightarrow {{\rm{V}}_{\rm{L}}} = 90{\rm{V}}\)

Now,  \({\rm{I}} = \frac{{{{\rm{V}}_{\rm{R}}}}}{{\rm{R}}} = \frac{{120}}{{1{\rm{k}}}} = 120 {\rm{mA}}\)

Again \({{\rm{V}}_{\rm{L}}} = {\rm{I}} \times{\rm{\omega L}}\)

\(\begin{array}{l} \Rightarrow 90 = 0.12 \times 500 \times {\rm{L}}\\ \Rightarrow {\rm{L}} = \frac{{90}}{{0.12 \times 500}} = 1.5{\rm{H}} \end{array}\)