1. Lecture 12-1 Resistors in Parallel and in Serial R1R1 R2R2 i i ε

2. Lecture 12-2 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

3. Lecture 12-3 Galvanometer Inside Ammeter and Voltmeter Ammeter: an instrument used to measure currents. Its total resistance is made very small by connecting a “shunt resistor” with very small resistance in parallel. Voltmeter: an instrument used to measure potential differences. Its total resistance is made very large by connecting to a resistor with very large resistance in parallel. galvanometer shunt resistor galvanometer Galvanometer: a device that detects small currents and indicates its magnitude.

4. Lecture 12-4 Ammeter and Voltmeter Ammeter: an instrument used to measure currents It must be connected in series. The internal resistance of an ammeter must be kept as small as possible. Then current is the same before and after plug the Ammeter Voltmeter: an instrument used to measure potential differences It must be connected in parallel. The internal resistance of a voltmeter must be made as large as possible. Then the current through R1 will be the same, i.e. potential drop across R1 will not be changed before and after plug the Voltmeter.

5. Lecture 12-5  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.

6. Lecture 12-6 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

7. Lecture 12-7 Charge Q(t) during Discharging 0.37Q 0 time constant

8. Lecture 12-8 Current I(t) during Discharging

9. Lecture 12-9 Broken circuit = RC 110V C very small. i.e. RC very small. Instantly discharged

10. Lecture 12-10 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

11. Lecture 12-11 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)

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

13. Lecture 12-13 Current I(t) during Charging 0.37I 0

14. Lecture 12-14 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

15. Lecture 12-15 Energy Conservation in Discharging a Capacitor Discharging: Energy lost by C Power dissipated by R

16. Lecture 12-16 Energy Conservation in Charging a Capacitor Charging: Work done by battery Energy stored in C The rest? Power dissipated by R  Indpendent of R

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

18. Lecture 12-18 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

19. Lecture 12-19 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