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ADV/TEC 5: Resonance. Introductory mini-lecture. Resonance in physical systems. Mechanical: pendulum, Tacoma Narrows bridge Atomic transitions: frequency of photon matches the energy difference between two atomic levels

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adv tec 5 resonance

ADV/TEC 5: Resonance

Introductory mini-lecture

resonance in physical systems
Resonance in physical systems
  • Mechanical: pendulum, Tacoma Narrows bridge
  • Atomic transitions: frequency of photon matches the energy difference between two atomic levels
  • Electrical: an LC circuit responds very sharply at a particular frequency

Resonance is a property of systems that have a natural frequency of oscillation. For example:

parallel lcr circuit
Parallel LCR circuit
  • Impedance of the capacitor decreases with frequency, so |iC| increases with frequency
  • Impedance of the inductor increases with frequency, so |iL| decreases with frequency
lcr circuit at resonance
LCR circuit at resonance
  • Impedance of inductor and capacitor in parallel:
  • At resonance ZL + ZC = jωL – j/ωC = 0,

i.e.,|ZL|=|ZC |whenω2 =1/LC or

  • Ztotal is (theoretically) infinite, so net current = 0,

i.e., iL= vL/ZL = –vC/ZC = –iC

vector representation
Vector representation
  • At resonance the vectors iL and iC are equal in magnitude but differ by 180⁰ in phase
  • Input and output voltages are equal
quality factor q of a resonant circuit
Quality factor Q of a resonant circuit
  • f1 and f2 are the frequencies at which |v2/v1| =
  • Q = f0/(f2 – f1) measures the sharpness of the resonance
  • Q measures the ratio of energy

stored to energy dissipated

  • Q is proportional to R, so need

large R for high Q

non ideal inductor
Non-ideal inductor
  • The Q of the resonance is also affected

by the resistance of the inductor RL

  • We represent RL as an equivalent parallel resistance R\'L so R and R\'L form a simple resistive voltage divider at resonance
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