340 Week 10: Maxwell’s Equations and Light
Your answer for Z should remind you of parallel addition of resistors, using reactances instead (two
of which areπ/2 out of phase with the resistor, of course).
Advanced Problem 9.
CLRThis problem is in two parts. First,for your own enduring benefitI wantyouto derive the
full solution to the drivenLRCcircuit problem. In particular, start with Kirchhoff’s rule for the
loop and either assume a complexV(t) =V 0 eiωtandI(t) =I 0 eiωt(where by conventionV 0 is real,
I 0 =|I 0 |e−iδ, and where one gets physical answers at theendby taking the real part of the complex
answers,orassumeV(t) =V 0 cos(ωt) andI(t) =I 0 cos(ωt−δ). Find an algebraic expression that
expresses the sum of the voltages. Solve this expression using either phasors (which will work in
both cases, one in the complex plane and one in a ”real” x-y plane) or inthe complex case directly
using algebra, no pictures really required.
Factor out the solution to obtain|I 0 |andδ,Z(the impedance), and the voltages across each
element as a function of time.