Solution Found!
(a) Transformvt__100 cos377t30_to phasor form. Comment on
Chapter , Problem 2.6(choose chapter or problem)
(a) Transform \(v(t)=100 \cos \left(377 t-30^{\circ}\right)\) to phasor form. Comment on whether \(\omega=377\) appears in your answer.
(b) Transform \(V=100 \angle 20^{\circ}\) to instantaneous form. Assume that \(\omega=377\).
(c) Add the two sinusoidal functions a(t) and b(t) of the same frequency given as follows: \(a(t)=\mathrm{A} \sqrt{2} \cos (\omega t+\alpha)\) and \(b(t)=\mathrm{B} \sqrt{2} \cos (\omega t+\beta)\). Use phasor methods and obtain the resultant c(t). Does the resultant have the same frequency?
Questions & Answers
QUESTION:
(a) Transform \(v(t)=100 \cos \left(377 t-30^{\circ}\right)\) to phasor form. Comment on whether \(\omega=377\) appears in your answer.
(b) Transform \(V=100 \angle 20^{\circ}\) to instantaneous form. Assume that \(\omega=377\).
(c) Add the two sinusoidal functions a(t) and b(t) of the same frequency given as follows: \(a(t)=\mathrm{A} \sqrt{2} \cos (\omega t+\alpha)\) and \(b(t)=\mathrm{B} \sqrt{2} \cos (\omega t+\beta)\). Use phasor methods and obtain the resultant c(t). Does the resultant have the same frequency?
ANSWER:Step 1 of 6
(a) It is given that,
The instantaneous value of voltage is, \(v(t)=100 \cos \left(377 t-30^{\circ}\right) V\)
From the expression of instantaneous voltage \(v(t)\)
The maximum value of voltage is, \(V_{\max }=100 \mathrm{~V}\)
The Phase angle is, \(\delta=-30^{\circ}\)
The angular frequency is, \(\omega=377\)