How is reactive power=VIsin(\$\phi\$)

Question

I know the active power is equal to average of power consume and is equal to VI cos(\$\phi\$). But how is apparent power VI and active power V sin(\$\phi\$). Is there any derivation.

Answer 1

how is apparent power VI and active power V sin(ϕ). Is there any derivation.

It's just a right angled triangle and trigonometry: -

Image from Electrician's Journal - Understanding Power Factor