1. Phy2005 Applied Physics II Spring 2016 Announcements: Solutions to previous day’s problems posted on HW page Answers to chapter 21 problems posted on HW page Exam 1 10 in class. 1 handwritten formula sheet ok PH gone Monday, Feb. 8; in-class review by Dr. Andy Linscheid PH Tuesday ofc. hr. cancelled, extra ofc. hour this Friday 3pm

2. Science news page Aurora Borealis http://www.aurorahunter.com/how-the-aurora-borealis-form.php

3. Last time: microscopic picture of conduction Ions E. Average speed of electrons in wire: about c/10: 2. Drift velocity of electrons: very slow, less than 1 cm/sec. This velocity corresponds to the current we calculate. 3. Velocity of information, energy flow. Close to c.

4. Today: T-dependence of resistance, Kirchoff’s laws Power = work done against electric forces/time P=IV for circuit element with current I through it and voltage V across it For resistor, V=IR, so also P=V 2 /R, I 2 R Caveat: remember what quantity is held fixed in a given circuit if something changes!!!

5. ACADEMIC HONESTY Each student is expected to hold himself/herself to a high standard of academic honesty. Under the UF academic honesty policy. Violations of this policy will be dealt with severely. There will be no warnings or exceptions.UF academic honesty policy

6. 55 44 33 A 12V battery is connected from a to b. Find the current that flows in the 3  resistor. a b 1. 5.2 Amp 2. 5.2 V 3. 2.3 Amp 4. 2.3 V 5. 4 Amp

7. If the four light bulbs in the figure are identical, which circuit puts out more light? 1. I 2. II 3. Same for both 4. Need to know R

8. r r r/2 2r P = V 2 /R PI = V 2 /(r/2) = 2V 2 /r PII = V 2 /(2r) = V 2 /(2r) = (1/4)PI

9. ACADEMIC HONESTY Each student is expected to hold himself/herself to a high standard of academic honesty. Under the UF academic honesty policy. Violations of this policy will be dealt with severely. There will be no warnings or exceptions.UF academic honesty policy

10. Ex Two different shape of wires are made out of copper. The first one has a 1 mm radius and 1 m long. The second wire has 0.5 mm radius and 25 cm long. Calculate their resistances.  copper = 1.7 x 10 -8  m R =  L/A R1 = R2 = 5.4 x 10 -3 

11. Spec: 40 W/120 V P = IV = V 2 /R = 40 (W) R = 120 2 /40 = 367 (  ) R measured ≈ 26  Why are they so different?

12.  Temperature However, insulators have the opposite tendency. The higher temperature, the lower R. metals insulators Operating bulb: 2550 degrees Celsius 367  Filament at room T: 25 degrees Celsius 26 

13.  depends on temperature!!!

14. In 1913, a ground breaking observation was made in a laboratory in Leiden (Netherlands). Kammerlingh Onnes Van der Waals Superconductivity!

15. Kirchoff’s Laws (1) Node rule, current law,.. I1I1 I2I2 I3I3 I 1 = I 2 + I 3 = +

16. (2) Loop rule, V-law,.. R1 R2 A BC D E F V A B C D E F A V

17. R1R2 V R3 I V IR 1 IR 2 IR 3 V – IR 1 – IR 2 – IR 3 = 0 V = I (R 1 + R 2 + R 3 ) = I R eq

18. V R1R2R3R1R2R3 I I1I1 I2I2 I3I3 4 unknowns Need 4 independent eqs. (1) I = I1 + I2 + I3 (2) V – I 1 R 1 = 0 (3) V – I 2 R 2 = 0 (4) V – I 3 R 3 = 0 V/R 1 = I 1 V/R 2 = I 2 V/R 3 = I 3 V (1/R 1 +1/R 2 +1/R 3 ) = I 1/R eq V = IR eq

19. How do we measure I or potential drop in a circuit? Measuring instruments should not change the values!! A V A A V Should have ideally zero internal resistance. Should have ideally infinite internal resistance.

20. RECIPE (1) Indicate currents going through each circuit elements: * Realize that the same I flows through elements up to the junction points. * Make your best educated guess on the directions of I’s. (2) The currents are your unknowns. * You have to set up the same number of indep. Eqs. * At least one of them come from the I-law and the rest of them are from the V-law (3) Set up the appropriate loops and apply V-law for each loop. The direction of each loop can be either CW or CCW. * If the loop runs from (-) to (+) of a battery, the battery contributes (+) voltage (vice versa). * If the loop runs in the same direction as that of your current, the resistor contributes (-) voltage calculated from Ohm’s Law (vice versa). * Add all the contributions from the elements (R’s and batteries) in the loop will be set to “0”. 1 equation. ++ After all, if you get (-) current value, that simply means the current flows in the direction opposite to your guess.

21. 5 3 6V 8 V I1 I2 I3 I1, I2, and I3 3 unknowns I 1 = I 2 + I 3 6 – 5*I 2 – 8 = 02 + 5*I 2 = 0I 2 = - 0.4 A 6 – 3*I 3 = 0I 3 = 2 A I 1 = 1.6 A This means that Your guess on the direction of I2 was wrong and actual current flows opposite direction.

22. Does Ohm’s law say this? Ohm: A liquid measure formerly used in Germany, varying locally between 30 and 36 gallons. With the same potential drop (voltage) applied, the larger current flows through the smaller resistance. With the same current flowing, larger potential drop develops across the larger resistance. If the resistance is infinite, no current flows regardless of potential (voltage) difference across the resistor. When there is no potential difference across an element, no current flows through regardless of the resistance. Yes, go check OED! Obvious! I = V/R Simple as V = IR

23. ACADEMIC HONESTY Each student is expected to hold himself/herself to a high standard of academic honesty. Under the UF academic honesty policy. Violations of this policy will be dealt with severely. There will be no warnings or exceptions.UF academic honesty policy

24. 24 V

25. 4050 1020 30 3 V4 V5 V I1 I2 I3 I 2 = I 1 + I 3 4 – 40I 1 – 3 – 10I 1 – 20I 2 = 01 – 50I 1 – 20I 2 = 0 4 – 50I 3 – 5 – 30I 3 – 20I 2 = 0-1 – 80I 3 – 20I 2 = 0 Example 21.3