RC Circuits

1 P12-Class 12: OutlineHour 1:Working with CircuitsExpt. 4. Part I: Measuring V, I, RHour 2:RC CircuitsExpt. 4. Part II: RC Circuits2 P12-Last Time:Resistors & Ohm’s Law3 P12-Resistors & Ohm’s LawRAρ=􀁁IRV=∆parallel12111RRR=+series12RRR=+4 P12-Measuring Voltage & CurrentP12-Measuring Potential DifferenceA voltmeter must be hooked in parallelacross the element you want to measure the potential difference acrossVoltmeters have a very large resistance, so that they don’t affect the circuit too muchP12-Measuring CurrentAn ammeter must be hooked in serieswith the element you want to measure the current throughAmmeters have a very low resistance, so that they don’t affect the circuit too muchP12-Measuring ResistanceAn ohmmeter must be hooked in parallelacross the element you want to measure the resistance ofHere we are measuring R1Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery)8 P12-Experiment 4:Part 1: Measuring V, I & R9 P12-RC Circuits10 P12-(Dis)Charging a Capacitor1.When the direction of current flow is toward the positive plate of a capacitor, thendQIdt=+Charging2. When the direction of current flow is away from the positive plate of a capacitor, thenDischargingdQIdt=−11 P12-Charging A CapacitorWhat happens when we close switch S?12 P12-Charging A CapacitorNO CURRENTFLOWS!0=−−=∆∑IRCQViiε1. Arbitrarily assign direction of current2. Kirchhoff (walk in direction of current):13 P12-Charging A CapacitorQdQRCdtε−=dQdtQCRCε⇒=−−00QtdQdtQCRCε=−−∫∫A solution to this differential equation is:()/()1tRCQtCeε−=−RCis the time constant, and has units of seconds14 P12-Charging A Capacitor/tRCdQIedtRε−==()/1tRCQCeε−=−15 P12-PRS Questions:Charging a Capacitor16 P12-Discharging A CapacitorWhat happens when we close switch S?17 P12-Discharging A CapacitorNO CURRENTFLOWS!dtdqI−=0=−=∆∑IRCqVii18 P12-Discharging A Capacitor 0dqqdtRC+=00QtQdqdtqRC⇒=−∫∫/()tRCoQtQe−=19 P12-General Comment: RCAll Quantities Either:()/FinalValue()Value1tteτ−=−/0Value()Valuetteτ−=τcan be obtained from differential equation (prefactoron d/dt) e.g. τ= RC20 P12-Exponential Decay/0Value()Valuetteτ−=Very common curve in physics/natureHow do you measure τ?1)Fit curve (make sure you exclude data at both ends)(t0,v0)(t0+τ,v0/e)2) a) Pick a pointb) Find point with y value down by ec) Time difference is τ21 P12-Demonstrations:RC Time Constants22 P12-Experiment 4:Part II: RC Circuits23 P12-PRS Question:Multiloopcircuit with Capacitor in One Loop