1. Lecture 12-1 Answer for the Warm-up quiz Replace by equivalent R=2  first. Sketch the diagram Simplify using equivalent resistors Label currents with directions Use Junction Rule in labeling Choose independent loops Use Loop Rule Solve simultaneous linear equations I 1 +I 2 I2I2 I1I1

2. Lecture 12-2  Capacitor in RC Circuits I charging I discharging  Switch closed at t=0. C initially uncharged, thus V 0 = 0 across C and I 0 =  /R initially.  Switch closed at t=0. C initially charged, thus V 0 = Q 0 /C across C and I 0 = V 0 /R initially.  After a long time, C is fully charged and V  =  across C and I  = 0.  After a long time, C is fully discharged and V  = 0 across C and I  = 0.

3. Lecture 12-3 Discharging a Capacitor in RC Circuits 2. Loop Rule: 3.Convert to a differential equation 4.Solve it! 1. Switch closed at t=0. Initially C is fully charged with Q 0 I RC is the time constant

4. Lecture 12-4 Charge Q(t) during Discharging 0.37Q 0 time constant

5. Lecture 12-5 Current I(t) during Discharging

6. Lecture 12-6 Broken circuit = RC 110V C very small. i.e. RC very small. Instantly discharged

7. Lecture 12-7 Broken circuit = RC 110V C very small. i.e. RC very small. Instantly discharged

8. Lecture 12-8 Warm-up quiz What’s the time constant in the following circuit. All resistors have the same resistance R, all capacitors have the same capacitance C. A.3/5RC B.2RC C.RC D.4/9RC E.6/4RC

9. Lecture 12-9 Charging a Capacitor in RC Circuits 1.Switch closed at t=0 C initially uncharged, thus zero voltage across C. 2. Loop Rule: 3. Convert to a differential equation 4.Solve it! (  =RC is the time constant again)

10. Lecture 12-10 Charge Q(t) during Charging time constant

11. Lecture 12-11 Current I(t) during Charging 0.37I 0

12. Lecture 12-12 Behavior of Capacitors Charging –Initially, the capacitor behaves like a wire. –After a long time, the capacitor behaves like an open switch. Discharging –Initially, the capacitor behaves like a battery. –After a long time, the capacitor behaves like an open switch

13. Lecture 12-13 Energy Conservation in Discharging a Capacitor Discharging: Energy lost by C Power dissipated by R

14. Lecture 12-14 Energy Conservation in Charging a Capacitor Charging: Work done by battery Energy stored in C The rest? Power dissipated by R  Indpendent of R

15. Lecture 12-15 PHYS241 - Quiz 12A All the capacitors below are identical and so are all the resistors. Which circuit has the shortest time constant? B D E A C

16. Lecture 12-16 PHYS241 - Quiz 12B All the capacitors below are identical and so are all the resistors. Which circuit have the longest time constant? AB D E C

17. Lecture 12-17 PHYS241 - Quiz 12C All the capacitors below are identical and so are all the resistors. Which circuit have the shortest time constant? A B C D E