Hi all.
Please take a look at the attachted circuit.
I have found the following expression for the complex current in the resistor (the hat indicates that it is complex):
\(\widehat_{I (t)} = \frac{{\omega ^2 LC {\widehat{U_0} }}}{{\omega ^2 LRC + i\omega L - R}}\exp ( - i\omega t),\)
where U_0 is the amplitude of U(t), and the hat indicates that it is complex.
Now I wish to find the real current, and I want to write it as:
\(I(t) = I_0\cos(\omega t + \phi).\)
But how do I do this? I have spent like 2 hours trying, but I don't
know how to rewrite the complex amplitude of the current to have a
phase.
Thanks in advance.
Regards
Niles.
Please take a look at the attachted circuit.
I have found the following expression for the complex current in the resistor (the hat indicates that it is complex):
\(\widehat_{I (t)} = \frac{{\omega ^2 LC {\widehat{U_0} }}}{{\omega ^2 LRC + i\omega L - R}}\exp ( - i\omega t),\)
where U_0 is the amplitude of U(t), and the hat indicates that it is complex.
Now I wish to find the real current, and I want to write it as:
\(I(t) = I_0\cos(\omega t + \phi).\)
But how do I do this? I have spent like 2 hours trying, but I don't
know how to rewrite the complex amplitude of the current to have a
phase.
Thanks in advance.
Regards
Niles.
Attachments
-
3.4 KB Views: 22