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 )?
For the first portion of your question, phasors are usually written in the following form, Where is the magnitude, omega is the frequency (in rad/s) and 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, ?
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 )?
Okay so for the first question again, it will be of the form, For the second question, I don't see how you get that j down there. So, Note, in simply a complex factor, the information we seek is representated by,
Its solved 1st one i have took it like 90-θ when i should take θ-90 ((ωt+10)-90) 2nd one, = cos90 + jsin90 = 0+j = j Thanks