Today’s Concept: RC Circuits Physics 2112 Unit 11 Today’s Concept: RC Circuits
RC Circuit (Charging) Kirchoff’s Voltage Rule Differential Equation Capacitor uncharged, Switch is moved to position “a” a R Vbattery C b R Vbattery C a b Kirchoff’s Voltage Rule Differential Equation Draw switch being closed Draw current at t = 0 Draw VC = 0 Reveal short term equation After long term, indicate IC = 0 implies VR = 0 Unit 11, Slide 2
Example 11.1 (Charging Capacitor) C1 = 1uF R1 = 1.2MW 10V What is the charge on the capacitor 1second after the switch is closed? What is the current through the resistor 1 second after the switch is closed? Conceptual Idea: Use charging equations for a capacitor. Note: e-1 = 0.37 1-e-1 = 0.63 Plan: Find time constant, t Find Qf and Io Put in t=1sec
Example 11.2 (Charging Capacitor) C1 = 1uF R1 = 1.2MW 10V What is the charge on the capacitor 10 seconds after the switch is closed? What is the current through the resistor 10 seconds after the switch is closed? Conceptual Idea: Use charging equations for a capactor. Plan: Find time constant, t Find Qf and Io Put in t=1sec
RC Circuit (Discharging) Capacitor has q0 = CV, Switch is moved to position “b” Kirchoff’s Voltage Rule R Vbattery C a b R Vbattery C a b I + - Differential Equation Counterclockwise current V -I Unit 11, Slide 5
Example 11.3 (Discharging Capacitor) C1 = 1uF R1 = 1.2MW 10V 1 The switch is held in position 1 for a long time and the capacitor becomes fully charged. It is then flipped to position 2. What is the charge on the capacitor 2 seconds after the switch is flipped? 2 Conceptual Idea: Use discharging equations for a capacitor. Plan: Find time constant, t Find Qo Put in t=2sec
How do Exponentials Work? “Fraction of initial charge that remains” Not all curves that look like are exponential!! “How many time constants worth of time that have elapsed” Unit 11, Slide 7
the longer it takes to get the same change… RC = 2 Time constant: t = RC The bigger t is, the longer it takes to get the same change… RC = 1 Unit 11, Slide 8