1P25-Class 25: Outline Hour 1: Expt. 10: Part I: Measuring L LC Circuits Hour 2: Expt. 10: Part II: LRC Circuit2P25-Last Time: Self Inductance3P25-Self InductanceLNI=Φ1. Assume a current I is flowing in your device2. Calculate the B field due to that I3. Calculate the flux due to that B field4. Calculate the self inductance (divide out I)dILdtε≡ −To Calculate:The Effect: Back EMF:Inductors hate change, like steady stateThey are the opposite of capacitors4P25-LR Circuitt=0+: Current is trying to change. Inductor works as hard as it needs to to stop itt=∞: Current is steady. Inductor does nothing.()/() 1tIt eRτε−=−5P25-LR Circuit: AC Output Voltage 0.00 0.01 0.02 0.03 0.00 0.05 0.10 0.15 0 1 2 3 ) ) Current -3 -2 -1 0 1 2 3 VollI (ATime (sInductor (V)tmeter across L Output (V) Output Vo tage6P25-Non-Ideal Inductors Non-Ideal (Real) Inductor: Not only L but also some R In direction of current: dIL IRdtε= −− =7P25-LR Circuit w/ Real Inductor Due to Resistance 1. Time constant from I or V 2. Check inductor resistance from V just before switch8P25-Experiment 10: Part I: Measure L, R STOP after you do Part I of Experiment 10 (through page E10-5)9P25-LC Circuits Mass on a Spring: Simple Harmonic Motion (Demonstration)10P25-Mass on a Spring22220dxFkxmamdtdxmkxdt=− = =+=00() cos( )xt x tωφ=+(1)(2)(3)(4)What is Motion?0Angular frequencykmω==Simple Harmonic Motionx0: Amplitude of Motionφ: Phase (time offset)11P25-Mass on a Spring: Energy00() cos( )xt x tωφ=+(1) Spring (2) Mass(3) Spring(4) MassEnergy has 2 parts: (Mass) Kinetic and (Spring) Potential222002220011sin ( )2211cos ( )22sdxKm kx tdtUkxkx tωφωφ⎛⎞== +⎜⎟⎝⎠== +00 0'( ) sin( )xt x tωωφ=− +Energy sloshes back and forth12P25-Simple Harmonic MotionAmplitude (x0)00() cos( )xt x tωφ=−1Period ( )frequency ( )2angular frequency ( )Tfπω==Phase Shift ( )2πϕ=13P25-Electronic Analog: LC Circuits14P25-Analog: LC CircuitMass doesn’t like to accelerateKinetic energy associated with motionInductor doesn’t like to have current changeEnergy associated with current2221;2dv d xFma m m E mvdt dt== = =2221;2dI d qLLELIdt dtε=− =− =15P25-Analog: LC CircuitSpring doesn’t like to be compressed/extendedPotential energy associated with compressionCapacitor doesn’t like to be charged (+ or -)Energy associated with stored charge21;2Fkx E kx=− =2111;2qE qCCε==1;;; ;FxqvImLkCε−→→→ →→16P25-LC Circuit resistor, and battery. 1. Set up the circuit above with capacitor, inductor, 2. Let the capacitor become fully charged. 3. Throw the switch from a to b 4. What happens?17P25-LC Circuit It undergoes simple harmonic motion, just like a mass on a spring, with trade-off between charge on capacitor (Spring) and current in inductor (Mass)18P25-PRS Questions: LC Circuit19P25-LC Circuit0 ; QdI dQLICdt dt−= =−2210 dQQdt LC+=00() cos( )Qt Q tωφ=+01LCω=Q0: Amplitude of Charge Oscillationφ: Phase (time offset)Simple Harmonic Motion20P25-LC Oscillations: Energy2220122 2EBQQUU U LICC=+= + =22200cos22EQQUtCCω⎛⎞==⎜⎟⎝⎠2222 2000 011sin sin22 2BQULILI t tCωω⎛⎞== =⎜⎟⎝⎠Total energy is conserved !!Notice relative phases21P25-Adding Damping: RLC Circuits22P25-Damped LC Oscillations Resistor dissipates energy and system rings down over time Also, frequency decreases: 2 2 0 ' 2 R Lω ω ⎛ ⎞ = −⎜ ⎟⎝ ⎠23P25-Experiment 10: Part II: RLC Circuit Use Units24P25-PRS Questions: 2 Lab
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