Any help with the question below would be very much appreciated and a worked solution would be appreciated even more! I think I have the correct answer for part a) and am on the right lines in part b) but I would love to be sure! Rep. will be awarded for good help!
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In a particular circuit the complex impedance, Z, is given in terms of the capacitance, C, inductance, L, resistance, R, and frequency, ω, by:
Z[w] = R + iωL + 1/(iωC)
C, L, R, ω are all real.
a)
Find in terms of L and C the value of the frequency, ω0, for which the impedance is real.
b)
Show that:
Z[w]/Z[ω0] = 1 + iQ(ω/ωo - ω0/ω.)
where Q is a real number.
c)
Find, in terms of ω0 and Q, the values of ω for which the ratio above has modulus √2.
d)
The complex voltage, V, and current, I, are related by V = Z[w]I. Find, in terms of Q, ω, ω0, the phase difference between V and I, i.e. Arg(V) - Arg(I).