Two circuits are shown in figure ( a ) and ( b ) . At a frequency...

For figure $( a )$

${P}_{avg} = {V}_{rms}^{2}R$

${v}_{rms}^{2}{Z}^{2} \times R = {v}_{rms}^{2}R \times 1$

${R}^{2} = {Z}^{2}$

$25 = {\left(\sqrt{{\left({x}_{C} - {x}_{L}\right)}^{2} + {5}^{2}}\right)}^{2}$

$25 = {\left({x}_{c} - {x}_{L}\right)}^{2} + 25$

${x}_{c} = {x}_{L} ⇒ \dfrac{1}{\omegaC} = \omegaL$

${\omega}^{2} = \dfrac{1}{LC} = \dfrac{{10}^{6}}{0 . 1 \times 40}$

$\omega = 500$