Question

Calculate P and Q for the following values. please answer in 3 signifiant values

v=60cos(ωt−15∘)Vv=60cos⁡(ωt−15∘)V,

i=5cos(ωt+60∘)Ai=5cos⁡(ωt+60∘)A.

v=420cos(ωt+30∘)Vv=420cos⁡(ωt+30∘)V,

i=30sin(ωt+240∘)Ai=30sin⁡(ωt+240∘)A.

v=200sin(ωt+250∘)Vv=200sin⁡(ωt+250∘)V,

i=5cos(ωt+40∘)Ai=5cos⁡(ωt+40∘)A.

Answer 1

1) Given V = 60 cos(wt-15)

i = 5 cos (wt + 60 ) A

Power P = 1/2 * V * i * cos($\Theta$V - $\Theta$ i)

P = 1/2*60 * 5 * cos( -15 - 60)

P = 1/2*60 * 5 * cos(-75)

P = 38.8225  W

Q = 1/2*V * i * sin($\Theta$V - $\Theta$ i)

Q = 1/2*60 *5 * sin( -15-60)

Q = 1/2*60 * 5* sin( -75)

Q = -144.888 VAR

2) V = 420 cos(wt + 30)

i = 30 sin(wt + 240)

I = 30 cos( 90 -(wt +240))

i = 30 cos( 90 -wt -240)

i = 30 cos( -wt-150)

i = 30 cos(wt +150)

Cos(-$\Theta$) = cos$\Theta$

i = 30 cos(wt +150) A

P =1/2* V * i * cso($\Theta$ V - $\Theta$ i)

P = 1/2*420 * 30 * cos( 30 -150)

P = 1/2*420 * 30 * cos(-120)

P = -3150  W

Q = 1/2*V*I * sin($\Theta$v - $\Theta$ i)

Q = 1/2*420 * 30 *sin( 30 -150)

Q = 1/2*420 * 30 *sin(-120)

Q = - 5455.96  VAR

3) V =200 sin(wt +250)

V = 200 cos(90-(wt+250)

V = 200 cos(90-wt-250)

V = 200 cos(-wt -160)

V = 200 cos( wt +160)

I = 5 cos(wt+ 40) A

P = 1/2*V * I * cos($\Theta$ V - $\Theta$ i)

P = 1/2*200 * 5 *cos( 160 -40)

P = 1/2*200*5 * cos(120)

P = -250 W

Q = 1/2*V * I * sin($\Theta$ V - $\Theta$ i)

Q = 1/2*200* 5* sin( 160 -40)

Q= 1/2*200* 5 * sin(120)

Q = 433.0125 VAR