Transcription of Chapter 31: RLC Circuits
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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) Calcu
RLC Circuit ÎThe loop rule tells us ÎUse i = dq/dt, divide by L ÎSolution slightly more complicated than LC case ÎThis is a damped oscillator (similar to mechanical case) Amplitude of oscillations falls exponentially 0 di q LRi dt C ++= 2 2 0 dq Rdq q dt Ldt LC ++= /2 ()2 max cos 1/ /2 qq e t LC R L=+=−−tR L ωθ ω′′
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