$C=100 \mu F, \frac{1}{\omega C}=\frac{1}{(100)\left(100 \times 10^{-6}\right)} $

$X _{ c }=100 \Omega, \quad X _{ L }=\omega L =(100)(.5)=50 \Omega $

$Z_1=\sqrt{x_C^2+100^2}=100 \sqrt{2} \Omega $

$Z_2=\sqrt{x_L^2+50^2}=\sqrt{50^2+50^2} $

$=50 \sqrt{2} $

$\varepsilon=20 \sqrt{2} \sin \omega t $

$i_1=\frac{20 \sqrt{2}}{100 \sqrt{2}} \sin (\omega t+\pi / 4) $

$i_1=\frac{1}{5} \sin (\omega t+\pi / 4) $

$I_2=\frac{20 \sqrt{2}}{50 \sqrt{2}} \sin (\omega t-\pi / 4) $

$I=\sqrt{(.2)^2+(.4)^2} $ 

$=(.2) \sqrt{1+4} $

$=\frac{1}{5} \sqrt{5}=\frac{1}{\sqrt{5}}$

$\text { (I) })_{m s}=\frac{1}{\sqrt{2} \sqrt{5}}=\frac{1}{\sqrt{10}}=\frac{\sqrt{10}}{10} $

$\approx 0.3 A $

$\left.\left(V_{100 n}\right)_{m 5}=\left(I_1\right)_{m 5}\right) \times 100 $

$=\left(\frac{0.2}{\sqrt{2}}\right) \times 100=\frac{20}{\sqrt{2}}=10 \sqrt{2} V $

$\left.V_{50 \Omega}\right)_{ ms }=\left(\frac{0.4}{\sqrt{2}}\right) \times 50=\frac{20}{\sqrt{2}}=10 \sqrt{2} V $