# Phasors

Discussion in 'Homework Help' started by wolf12, Apr 29, 2011.

1. ### wolf12 Thread Starter New Member

Apr 18, 2011
3
0
i = 4 sin(10t + 10◦)
Which phasor correct for the sinusoidal above?
1. magnitude = 4 phase = -80◦
2. maginitude = 4 phase = 100◦ (this is my answer, is it wrong ? why?)

2nd problem

dv/dt = −ωVm sin(ωt + φ) = ωVm cos(ωt + φ + 90◦)

= Re(ωVm * e^jωt * e^jφ * e^j90◦ ) = Re(j * ω * V * e^jωt )

how did j appear in Re(j ω V e^jωt )?

2. ### jegues Well-Known Member

Sep 13, 2010
735
43
For the first portion of your question, phasors are usually written in the following form,

$V_{m}sin( \omega t + \phi)$

Where $V_{m}$ is the magnitude, omega is the frequency (in rad/s) and $\phi$ is the phase shift.

For the second part of your question, are you trying to figure out what the derivative of this phasor is, like so,

$\frac{d}{dt}\left( -\omega V_{m}sin( \omega t + \phi) \right)$

?

3. ### wolf12 Thread Starter New Member

Apr 18, 2011
3
0
1st question - Very sorry , its polar form, i cudnt find that angle symbol here, so i wrote magnitude = .. phase =..

2nd question - Sorry Again,
v(t) = Re(V * e^jωt ) = Vm cos (ωt+φ),

dv/dt = −ωVm sin(ωt + φ) = ωVm cos(ωt + φ + 90◦)

= Re(ωVm * e^jωt * e^jφ * e^j90◦ ) = Re(j * ω * V * e^jωt )

how did j appear in Re(j ω V e^jωt )?

4. ### jegues Well-Known Member

Sep 13, 2010
735
43
Okay so for the first question again, it will be of the form,

$V_{m} \quad \angle \phi$

For the second question, I don't see how you get that j down there.

$\frac{dv}{dt} = \omega V_{m}cos(\omega t + \phi + \beta), \quad \text{ Where, } \beta = 90^{o}$

So,

$Re \left{ V_{m}e^{j(\phi + \beta)}e^{jwt} \right}$

Note, $e^{jwt}$ in simply a complex factor, the information we seek is representated by,

$\overline{V} = V_{m}e^{j(\phi - \beta)}} = V_{m} \angle (\phi - \beta)$

Last edited: Apr 29, 2011
5. ### wolf12 Thread Starter New Member

Apr 18, 2011
3
0
Its solved 1st one i have took it like 90-θ when i should take θ-90 ((ωt+10)-90)

2nd one,
$e^{j90}$ = cos90 + jsin90 = 0+j = j

Thanks