Transcription of Chapter 31: RLC Circuits
{{id}} {{{paragraph}}}
Example: barber
Chapter 31: RLC Circuits
PHY2049: Chapter 311 Chapter 31: RLC CircuitsPHY2049: Chapter 312 Topics LC Oscillations Conservation of energy Damped oscillations in RLC Circuits Energy loss AC current RMS quantities Forced oscillations Resistance, reactance, impedance Phase shift Resonant frequency Power Transformers Impedance matchingPHY2049: Chapter 313LC Oscillations Work out equation for LC circuit (loop rule) Rewrite using i = dq/dt (angular frequency) has dimensions of 1/t Identical to equation of mass on springLC0qdiLCdt =2222200dq qdqLqCdtdt += + =2222200dxdxmkxxdtdt += + =1LC =km =PHY2049: Chapter 314LC Oscillations (2) Solution is same as mass on spring oscillations qmaxis the maximum charge on capacitor is an unknown phase (depends on initial conditions) Calculate current: i = dq/dt Thus both charge and current oscillate Angular frequency , frequency f = /2 Period: T = 2 / Current and charge differ in phase by 90 ()maxcosqqt =+()()maxmaxsinsiniqtit = + = +km =PHY2049: Chapter 315 Plot Charge and Current vs t()maxcosqqt =()maxsiniit = tPHY2049: Chapter 316 Energy Oscillations in LC Circuits Total energy in circuit is conserved.
PHY2049: Chapter 31 9 LC Circuit Example ÎParameters C = 20μF L = 200 mH Capacitor initially charged to 40V, no current initially ÎCalculate ω, f and T ω= 500 rad/s f = ω/2π= 79.6 Hz T = 1/f = 0.0126 sec ÎCalculate q max and i max q max = CV = 800 μC = 8 ×10-4 C i max = ωq max = 500 ×8 ×10-4 = 0.4 A ÎCalculate maximum energies U C ...
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: