Class 12: OutlineLast Time:Resistors & Ohm’s LawResistors & Ohm’s LawMeasuring Voltage & CurrentMeasuring Potential DifferenceMeasuring CurrentMeasuring ResistanceExperiment 4:Part 1: Measuring V, I & RRC Circuits(Dis)Charging a CapacitorCharging A CapacitorCharging A CapacitorCharging A CapacitorCharging A CapacitorPRS Questions:Charging a CapacitorDischarging A CapacitorDischarging A CapacitorDischarging A CapacitorGeneral Comment: RCExponential DecayDemonstrations:RC Time ConstantsExperiment 4:Part II: RC CircuitsPRS Question:Multiloop circuit with Capacitor in One Loop1P12-Class 12: OutlineHour 1:Working with CircuitsExpt. 4. Part I: Measuring V, I, RHour 2:RC CircuitsExpt. 4. Part II: RC Circuits2P12-Last Time:Resistors & Ohm’s Law3P12-Resistors & Ohm’s LawRAρ=AIRV=∆parallel 1 2111RRR=+series 1 2RRR=+4P12-Measuring Voltage & CurrentP12-Measuring Potential DifferenceA voltmeter must be hooked in parallel across 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 series with 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 parallel across 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)8P12-Experiment 4:Part 1: Measuring V, I & R9P12-RC Circuits10P12-(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=−11P12-Charging A CapacitorWhat happens when we close switch S?12P12-Charging A CapacitorNO CURRENTFLOWS!0=−−=∆∑IRCQViiε1. Arbitrarily assign direction of current2. Kirchhoff (walk in direction of current):13P12-Charging A CapacitorQdQRCdtε−=dQ dtQC RCε⇒=−−00QtdQ dtQC RCε=−−∫∫A solution to this differential equation is:()/() 1tRCQt C eε−=−RC is the time constant, and has units of seconds14P12-Charging A Capacitor/tRCdQIedt Rε−==()/1tRCQC eε−=−15P12-PRS Questions:Charging a Capacitor16P12-Discharging A CapacitorWhat happens when we close switch S?17P12-Discharging A CapacitorNO CURRENTFLOWS!dtdqI −=0=−=∆∑IRCqVii18P12-Discharging A Capacitor 0dq qdt RC+=00QtQdq dtqRC⇒=−∫∫/()tRCoQt Qe−=19P12-General Comment: RCAll Quantities Either:()/FinalVal ue( ) Val ue 1tteτ−=−/0Value( ) Valuetteτ−=τ can be obtained from differential equation (prefactor on d/dt) e.g. τ = RC20P12-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 τ21P12-Demonstrations:RC Time Constants22P12-Experiment 4:Part II: RC Circuits23P12-PRS Question:Multiloop circuit with Capacitor in One
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