W12D2 RC, LR, in addition to Undriven RLC Circuits; Experiment 4 Announcements Outline RC Circuit Charging RC Circuit: Discharging
Grehan, Rick, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal W12D2 RC, LR, in addition to Undriven RLC Circuits; Experiment 4 Todays Reading Course Notes: Sections 11.7-11.9, 11.10, 11.13.6; Expt. 4: Undriven RLC Circuits Announcements Math Review Week 13 Tuesday 9pm-11 pm in 26-152 PS 9 due Week 13 Tuesday at 9 pm in boxes outside 32-082 or 26-152 Next Reading Assignment W12D3 Course Notes: Sections 11.8-9, 11.12-11.13 Outline Experiment 4: Part 1 RC in addition to LR Circuits Simple Harmonic Oscillator Undriven RLC Circuits Experiment 4: Part 2 Undriven RLC Circuits
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RC Circuit Charging Solution to this equation when switch is closed at t = 0: RC Circuit: Discharging Solution to this equation when switch is closed at t = 0 time constant: RL Circuit: Increasing Current Solution to this equation when switch is closed at t = 0: (units: seconds)
RL Circuit: Decreasing Current Solution to this equation when switch is opened at t = 0: (units: seconds) Measuring Time Constant Pick a point 1 with Find point 2 such that By definition then 2) In the lab you will plot semi-log in addition to fit curve (make sure you exclude data at both ends) Experiment 4: RC in addition to RL Circuits
Mass on a Spring: Simple Harmonic Motion Demonstration Mass on a Spring: Simple Harmonic Motion Mass on a Spring (C 2) http://scripts.mit.edu/~tsg/www/demo.phpletnum=C%202&show=0 Mass on a Spring (1) (2) (3) (4) What is Motion Simple Harmonic Motion x0: Amplitude of Motion f: Phase (time offset)
Simple Harmonic Motion Amplitude (x0) Concept Question: Simple Harmonic Oscillator Which of the following functions x(t) has a second derivative which is proportional to the negative of the function 1. 2. 3. 4. Concept Question Answer: Simple Harmonic Oscillator Answer 4. By direct calculation, when
Mass on a Spring: Energy (1) Spring (2) Mass (3) Spring (4) Mass Energy has 2 parts: (Mass) Kinetic in addition to (Spring) Potential Energy sloshes back in addition to as long as th LC Circuit Set up the circuit above with capacitor, inductor, resistor, in addition to battery. Let the capacitor become fully charged. Throw the switch from a to b. What happens LC Circuit It undergoes simple harmonic motion, just like a mass on a spring, with trade-off between charge on capacitor (Spring) in addition to current in inductor (Mass). Equivalently: trade-off between energy stored in electric field in addition to energy stored in magnetic field.
Energy stored in electric field Energy stored in magnetic field Energy stored in electric field Energy stored in magnetic field Concept Question: LC Circuit Consider the LC circuit at right. At the time shown the current has its maximum value. At this time: the charge on the capacitor has its maximum value. the magnetic field is zero. the electric field has its maximum value. the charge on the capacitor is zero. Concept Q. Answer: LC Circuit Answer: 4. The current is maximum when the charge on the capacitor is zero Current in addition to charge are exactly 90 degrees out of phase in an ideal LC circuit (no resistance), so when the current is maximum the charge must be identically zero.
LC Circuit: Simple Harmonic Oscillator Charge: Angular frequency: Amplitude of charge oscillation: Phase (time offset): Simple harmonic oscillator: LC Oscillations: Energy Total energy is conserved !! Notice relative phases LC Circuit Oscillation Summary
Adding Damping: RLC Circuits Demonstration Undriven RLC Circuits (Y 190) RLC Circuit: Energy Changes Include finite resistance: Multiply by Decrease in stored energy is equal to Joule heating in resistor
Damped LC Oscillations Resistor dissipates energy in addition to system rings down over time. Also, frequency decreases: Experiment 4: Part 2 Undriven RLC Circuits Appendix: Experiment 4: Part 2 Undriven RLC Circuits Group Problem in addition to Concept Questions
Concept Question Answer: LC Circuit Answer: 1. It will increase (decay more rapidly) Resistance is what dissipates power in the circuit in addition to causes the amplitude of oscillations to decrease. Increasing the resistance makes the energy ( in addition to hence amplitude) decay more rapidly.
Grehan, Rick Contributing Editor
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