Question

The power consumed in W

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$

$P=i^{2}R=\left(5.5{)}^2\right(39.26)$$=1187.6W=1.188kW$