Question

A certain circuit has equivalent impedance Z = 3+j4 Ω, and an applied voltage

v = 50 cos( 1000t +30°) V The apparent power S is

select one:

a. 180.6L 53.13°VA

b. 302.5L53.13°VA

C. 360L 53.13°VA

d. 202.52L53.13°VA

e. 250L53.13°VA

Answer 1

The apparent power is

$$S=V\text{conjg}[I]=V\text{conjg}\bigg[\frac{V}{Z}\bigg],\\\space\\ S=\bigg(\frac{50}{\sqrt2}\angle30°\bigg)\text{conjg}\bigg[\frac{\frac{50}{\sqrt2}\angle30°}{3+j4}\bigg]= 250\angle53.13°\text{VA}.$$