Question

Part a:Why are the phases across each individual component (capacitor, resistor, inductor) what they are?

Advice:            

• Start with formula ϕ=arctan(ω0^2−ω^2/γω)

for ϕ above, and consider it at the resonant frequency. (Or, equivalently, consider the phasor diagram at resonance; the phase shift ϕ is the same as the phase of the signal in that diagram.)                

Then, figure out how the different circuit components' phases should relate to Q(t)

, and thus how they relate to ϕ

• .                

• You can also make a more physically-motivated explanation, based on an intuitive analogy to mechanical resonance and simple harmonic oscillation (where "pushing on a swing" is a good picture). This is by no means required, though.            

           

Part B: Why is the voltage across the resistor what it is? Why is the voltage across the inductor-capacitor combination what it is?            

Part C: Why are these not exactly what you would expect (theoretically-speaking)? (Hint: the phase of the L+C contribution may be a hint as to what we are neglecting.)            

Part D: How can the voltage amplitude across the capacitor and inductor (individually) be larger than the input voltage? Where does the energy come from?

Answer 1