Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
PHYS219 Fall semester 2014 Lecture 09: RC Circuits; Magnetism Dimitrios Giannios Purdue University First Midterm (EXAM I) • Date: Thursday, September 25 @ 8pm • Place: Physics, Room 112 • Duration: 1 hour • Material Chapters 17, 18, 19 from coursebook • as covered in classroom • Do NOT bring your own “cheat sheet” (relevant equations will be provided) • All cell phones/smart phones are to be deactivated Circuits with capacitor The capacitance C of a capacitor tells about its ability to store charge from experiment: I q∝ ΔV q = C ΔV q=CV The RC Circuit – Charging the Capacitor • Kirchhoff’s Rules can be applied to all kinds of circuits • The change in the potential around the circuit is • What is I? • What’s new?: I (and q) will now be time dependent Solving for q(t) and I(t) constant number Dq q e + - =0 Dt RC R Solving this equation is a four-step process: See Appendix 1. Solve: 2. A second solution is: 3.The most general solution will be: 4.Boundary Condition at t=0: unknown constant How to Realize the Boundary Conditions ? Boundary Conditions: at t=0, q(t=0)=0 How does q vary with time AFTER switch is closed? q The current cannot last forever. Why? ??? ??? t=0 t Summary of Results • The current in the circuit is described by • The voltage across the capacitor is • The charge is given by • τ = RC and is called the time constant Example E=9V R=10, 000 Ω C=0.001 F τ = RC=(R=10,000 Ω)(0.001 F)=10 s Units: [Ω][F]=[V/A][C/V]=[C/A]=s What is i) charge on the capacitor, ii) the voltage on the capacitor, iii) the current in the circuit, and iv) the voltage across the resistor 2 s after switch is closed? Capacitor Resistor Magnetism Name derived from rocks (lodestones, naturally magnetized pieces of iron ore) found in the province of Magnesia in Greece First reports – 2500 BC Historically, more interesting than electricity due to importance in early navigation applications Originally thought to be separate topic from electrostatics/electricity Today: Unified subject – electromagnetism Fundamental Property of Magnets South ‘seeking’ pole North ‘seeking’ pole Magnetic ‘dipole’ Magnetic Poles Force between Magnets Magnitude of force depends on pole strength Action at a Distance Gravity, electrostatic and magnetic forces are non-contact forces. They act on objects that are not touching each other. A force field describes these actionat-a-distance forces. Gravitational Field Electric Field (E) Magnetic Field (B) Magnetic Field/Electric Field for Dipoles Magnetic Field Lines B Electric Field Lines E Units: Tesla Units: N/C or V/m B is a vector 1 1 B lines continuous E is a vector E lines begin/end on sources/sinks Key Point: No ‘magnetic’ charges! Magnetic Field Strengths (typical values) Situation Magnetic Field (Tesla) Magnetic Field (Gauss) Interstellar space ~ 1 x 10-10 T ~ 1μ G Earth’s Field ~ 0.5 x 10-4 T ~ 0.5 G Bar Magnet (refrigerator) ~ 0.01 T ~ 100 G Laboratory Electromagnet ~ 2 T 20,000 G MRI unit (Hospital) ~ 0.5-3 T 5,000 – 30,000 G Large Superconducting Magnet ~ 20 T Pulsed Fields (non-destructive) ~ 100 T Explosive Compression (destructive) ~ 105 G ~ 1000 T White Dwarfs ~10-104 T Neutron Stars ~106-1011 T up to 108 G up to 1015 G!!! 10,000 Gauss = 1 Tesla The earth acts like large magnet Geographic N pole of earth roughly corresponds to Geomagnetic S pole of earth Earth’s Magnetic Field Earth’s Geomagnetic Pole wanders over time Magnetic Declination in Indiana is about 3o W Earth’s Magnetic Field & Northern lights Most powerful Cosmic Magnets Magnetized, Rotating Neutron Stars (~1012 G) Magnetars (~1015 G) APPENDIX: The exponential function vs. time At any time t, the f(t) = e t exponential function has a slope that is everywhere equal to the function itself Important Limits: