written 3.5 years ago by |
$\bar Z=12+j16\Omega \\ \bar Z=10-j20\Omega \\ V=230\ V$
$Let\ \ \bar V=230\lt 0^{\circ}V$
$\bar I_1=\dfrac{\bar V}{\bar Z_1}=\dfrac{230\lt 0^{\circ}}{12+j16}=11.5\lt -53.13^{\circ}\ A$
$\bar I_2=\dfrac{\bar V}{\bar Z_2}=\dfrac{230\lt 0^{\circ}}{10-j20}=10.29\lt 63.43^{\circ}\ A$
(i) kW, kVA, kVAR and power factor of branch 1
$P_1=VI_1cos\phi _1=230\times 11.5\times cos(53.13^{\circ})=1.59\ kW\\ S_1=VI_1=230\times 11.5=2.65\ kVA\\ Q_1=VI_1sin\phi _1=230\times 11.5\times sin(53.13^{\circ})=2.12\ kVAR\\ pf_1=cos\phi _1=cos(53.13^{\circ})=0.6\ (lagging)$
(ii) kW, kVA, kVAR, and power factor of branch 2
$P_2=VI_2cos\ \phi_2=230\times 10.29\times cos(63.43^{\circ})=1.06\ kW\\ S_2=VI_2=230\times 10.29=2.37\ kVA\\ Q_2=VI_2sin\phi _2=230\times 10.29\times sin(63.43^{\circ})=2.12\ kVAR\\ pf_2=cos\phi _2=cos(63.43^{\circ})=0.447\ (leading)$