1. Lecture 10-1 ©2008 by W.H. Freeman and Company

2. Lecture 10-2 Capacitor Examples 2C2C C C C/2 CCCC C ?C?C ?=2/3

3. Lecture 10-3 READING QUIZ 1 An electric toaster (resister) uses 2000 watts when the it is connected to a 100 volt potential difference. What is the resistance R (Ω) of the toaster? A| 10 Ω B| 5 Ω C| 15 Ω D| 20 Ω E| 12 Ω

4. Lecture 10-4 DOCCAM 2 DEMO 5B-01 OHMS LAW BOARD

5. Lecture 10-5 DOCCAM 2 DEMO 5B-O3 VOLTAGE PARADOX

6. Lecture 10-6 Electric Current Current = charges in motion Magnitude rate at which net positive charges move across a cross sectional surface Units: [I] = C/s = A (ampere) Current is a scalar, signed quantity, whose sign corresponds to the direction of motion of net positive charges by convention J = current density (vector) in A/m²

7. Lecture 10-7 Microscopic View of Electric Current in Conductor All charges move with some velocity v e random motion with high speeds (O(10 6 )m/s) but with a drift in a certain direction on average if E is present Drift velocity v d is orders of magnitudes less than the actual velocity of charges. A Why random motion? thermal energy scattering off each other, defects, ions, …

8. Lecture 10-8 Current and Drift Velocity in Conductor where n =carrier density or Drift velocity v d is orders of magnitudes less than the actual velocity of charges. if ohmic

9. Lecture 10-9 Ohm’s Law Summary Current-Potential (I-V) characteristic of a device may or may not obey Ohm’s Law: or V = IR with R constant Resistance (ohms) gas in fluorescent tube tungsten wire diode

10. Lecture 10-10 Resistance and Resitivity for Ohmic Material (= I/A if current density is uniform) L A resistivity R (in) Ohms Ω resistance

11. Lecture 10-11 Resistance constant R Ohm’s Law Resistance (definition) V R I

12. Lecture 10-12 Warm up quiz 2 There are 2x10 14 electrons entering a resistor in10 seconds. What is the current through the resistor? a) 2.0 μA b) 1.6  A c) 3.2 nA d) 1.6 A e) 3.2 μA Note: e = 1.6x10 -19 C V R I

13. Lecture 10-13 Temperature Dependence of Resistivity Materialρ 0 (Ωm)α (K -1 ) Ag1.6x10 -8 3.8x10 -3 Cu1.7x10 -8 3.9x10 -3 Si6.4x10 2 - 7.5x10 -2 glass10 10 ~ 10 14 sulfur10 15 Copper Usually T 0 is 293K (room temp.) Usually α > 0 (ρ increases as T )

14. Lecture 10-14 Electric Current and Joule Heating Free electrons in a conductor gains kinetic energy due to an externally applied E. electron gas Scattering from the atomic ions of the metal and other electrons quickly leads to a steady state with a constant current I. Transfers energy to the atoms of the solid (to vibrate), i.e., Joule heating. Mean drift of electrons, i.e., current

15. Lecture 10-15 Energy in Electric Circuits So, Power dissipation = rate of decrease of U = Steady current means a constant amount of charge ΔQ flows past any given cross section during time Δt, where I= ΔQ / Δt. Energy lost by ΔQ is => heat V

16. Lecture 10-16 EMF – Electromotive Force An EMF device is a charge pump that can maintain a potential difference across two terminals by doing work on the charges when necessary. Examples: battery, fuel cell, electric generator, solar cell, fuel cell, thermopile, … Converts energy (chemical, mechanical, solar, thermal, …) into electrical energy.  Within the EMF device, positive charges are lifted from lower to higher potential.  If work dW is required to lift charge dq, EMF

17. Lecture 10-17 Energy Conservation A circuit consists of an ideal battery (B) with emf ε, a resistor R, and two connecting wires of negligible resistance. Energy conservation Work done by battery is equal to energy dissipated in resistor Ideal battery: no internal energy dissipation EMF ε = terminal voltage V Real battery: internal energy dissipation exists dW > i 2 Rdt then εi > iR=V

18. Lecture 10-18 DOCCAM 2 DEMO 5B-02 TERMINAL VOLTAGE ON A BATTERY

19. Lecture 10-19 Resistors in Series  The current through devices in series is always the same. R1R1 R2R2 i i ε R eq i ε For multiple resistors in series:

20. Lecture 10-20 Internal Resistance of a Battery internal resistance terminal voltage load Life story (ups and downs) of a charge

21. Lecture 10-21 Lecture 10:30 quiz 3 September 22, 20ll There are 10 14 electrons entering in 10 seconds a resistor which has a potential drop of 3.2μV. What is the resistance of the resistor? a) 4.0 Ω b) 1.0 mΩ c) 2.0 Ω d) 3.0 μΩ e) 2.0 kΩ Note: e = 1.6x10 -19 C V R I

22. Lecture 10-22 Lecture 11:30 quiz 3 September 22, 2011 There are 10 14 electrons entering a resistor of resistance 1.0 Ω in 10 seconds. What is the potential drop across the resistor? a) 3.2 mV b) 8.0 V c) 2.5 V d) 1.6 μV e) 1.6 mV Note: e = 1.6x10 -19 C V R I

23. Lecture 10-23 Lecture 11:30 quiz 3 February 10, 2011 The potential drop is 6.4  V across a resistor of resistance 1.0Ω. How many electrons enter the wire in 5 seconds? a)3.2×10 14 b)8.0×10 15 c)2.5×10 12 d)2.0×10 17 e)1.6×10 19 Note: e = 1.6x10 -19 C V R I