Question

The current is given as $\frac{x}{10}A$. Find $x$

Answer 1

$Z_1=\frac{115}{3}=38.33\Omega$
$\cos {\varphi }_1=\frac{R_1}{Z_1}$
$\Rightarrow R_1=Z_1\cos {\varphi }_1$
$=\left(38.33\right)\left(0.6\right)=23\Omega$
$X_L=\sqrt{Z_1^2-R_1^2}=30.67\Omega$
$Z_2=\frac{115}{5}=23\Omega$
$R_2=Z_2\cos {\varphi }_2=\left(23\right)\left(0.707\right)$
$=16.26\Omega$
When connected in series
$R=R_1+R_2=39.26\Omega$
$X_L-X_C=14.41\Omega$
$\therefore Z=\sqrt{R^2+(X_L-X_C{)}^2}$
$=41.82\Omega$
$i=\frac{V}{Z}=\frac{230}{41.82}=5.5A$