Answer:
Explanation:
Given that:
v(t) = 339.4 sin(377t + 90°) V
i(t) = 5.657 sin (377t + 60°) A
v = 339.4 ∠ 90° [tex]v_m \angle\phi_1[/tex]
i = 5.657∠60° [tex]I_m \angle \phi_2[/tex]
The phase difference [tex]\phi = 90 -60[/tex] = 30
The average power [tex]P_{avg}[/tex] can be expressed as:
[tex]P_{avg} = \dfrac{v_m}{\sqrt{2}}\dfrac{I_m}{\sqrt{2}} \times cos (30)[/tex]
[tex]P_{avg} = \dfrac{339.4}{\sqrt{2}}*\dfrac{5.657}{\sqrt{2}} \times cos (30)[/tex]
[tex]\mathbf{P_{avg} = 831.38 \ watts}[/tex]
The reactive power Q is as follow;
[tex]Q = \dfrac{v_m}{\sqrt{2}} * \dfrac{I_m}{\sqrt{2}} \ sin \phi\\[/tex]
[tex]Q = \dfrac{339.4}{\sqrt{2}}*\dfrac{5.657}{\sqrt{2}} \times sin (30)[/tex]
Q = 479.99 VAR
The complex power S = P + jQ
The complex power S = 831.38 W + j479.99 VAR
