Question

Find the complex power, average power, and reactive power for the following:

Answer 1

Answer:

Explanation:

Given that:

v(t) = 339.4 sin(377t + 90°) V

i(t) = 5.657 sin (377t + 60°) A

v = 339.4 ∠ 90°      $v_m \angle\phi_1$

i = 5.657∠60°         $I_m \angle \phi_2$

The phase difference $\phi = 90 -60$ = 30

The average power $P_{avg}$ can be expressed as:

$P_{avg} = \dfrac{v_m}{\sqrt{2}}\dfrac{I_m}{\sqrt{2}} \times cos (30)$

$P_{avg} = \dfrac{339.4}{\sqrt{2}}*\dfrac{5.657}{\sqrt{2}} \times cos (30)$

$\mathbf{P_{avg} = 831.38 \ watts}$

The reactive power Q is as follow;

$Q = \dfrac{v_m}{\sqrt{2}} * \dfrac{I_m}{\sqrt{2}} \ sin \phi$

$Q = \dfrac{339.4}{\sqrt{2}}*\dfrac{5.657}{\sqrt{2}} \times sin (30)$

Q = 479.99 VAR

The complex power S =  P + jQ

The complex power S = 831.38 W + j479.99 VAR