- #1
yosimba2000
- 206
- 9
I know that when you get a current from a voltage (like calculating current through resistor), the current and voltage equations have the same frequency. Does this still hold for power P = VI ?
So assume V in Euler form, V(t) = Vcos(wt+theta) + jVsin(wt+theta) = V*ej(wt+theta) and in Phasor, V<theta = Vcos(wt+theta)
And assume I in Euler form, I(t) = Icos(wt+phi) + jIsin(wt+phi) = I*ej(wt+phi) and in Phasor, I<phi = Icos(wt+phi)
Then P = V(t)*I(t) = V*ej(wt+theta) * I*ej(wt+phi)
To get P = VI*ejwt+jwt+jphi+jtheta, call jphi + jtheta = jpsi
Then P = VI *e2jwt+jpsi
Then P = VI *ej(2wt+psi)
Then P = VIcos(2wt+psi)+jVIsin(wt+psi)
Real component is what we want, so P = VIcos(2wt+psi)
2wt (power frequency) isn't the same as wt (the frequency of current and voltage). Did I get the right result?
So assume V in Euler form, V(t) = Vcos(wt+theta) + jVsin(wt+theta) = V*ej(wt+theta) and in Phasor, V<theta = Vcos(wt+theta)
And assume I in Euler form, I(t) = Icos(wt+phi) + jIsin(wt+phi) = I*ej(wt+phi) and in Phasor, I<phi = Icos(wt+phi)
Then P = V(t)*I(t) = V*ej(wt+theta) * I*ej(wt+phi)
To get P = VI*ejwt+jwt+jphi+jtheta, call jphi + jtheta = jpsi
Then P = VI *e2jwt+jpsi
Then P = VI *ej(2wt+psi)
Then P = VIcos(2wt+psi)+jVIsin(wt+psi)
Real component is what we want, so P = VIcos(2wt+psi)
2wt (power frequency) isn't the same as wt (the frequency of current and voltage). Did I get the right result?