Can we find C in Section 2, Question 1 using just the equation for theresonant frequency, ωo=1/√LC?
Unfortunately, life is not so simple. There are at least four series/parallel transformations involved in finding the appropriate C: • Transform one of the inductors and its series resistance toparallel, in order to absorb the 50 Ω load seen at the tapping point.For this step, use the Q of the inductor itself. • After incorporating the 50 Ω, transform the new parallelresistance and the corresponding inductance back to series. Remember the Qwill have changed since you have added a new element (the 50 Ω). • Add up the series resistances and inductances and calculate thenew Q for the combined R and L. • Finally, convert the series L and R into parallel L and R, so thatyour net result is a parallel LRC circuit. Only when you have a parallel LCR circuit can you apply the 1/√LC equation; don’t forget the 2π term in ωo! Yes, this looks like a lot of work, but take heart – the resulting R in theparallel case is the Rt you need for Section 2, Question 3, and the final Q in the last step above i
