1. Lectures 8,9 (Ch. 25) Electric Current 1. Drift velocity 2. Ohm’s law 3. Volt-Amper characteristics 4. Thermal dependence of resistance 5. Resistors in series and parallel 6. Electric power 7.emf, battery 8.Simple circuits

2. Caution So far we studied electrostatics (equilibrium) Now we start to study electric current (nonequilibrium state) The following statements are not correct in the presence of electric current: 1. E inside conductors=0 Electric charges reside on the outer surface of conductor 2. Inside conductors V=const=V surface

3. Drift velocity Drift velocity does depend on a sign of charges + ions in plasmas or electrolytes, holes in semiconductorsElectrons in metals, - ions in plasmas, etc.

4. Electric current is a flow of charges (charge transferred per unite time via a given cross section) If different types of carriers present:

5. Ohm’s Law: Georg Ohm (1787 - 1854). Resistance SI unite of R: [R]=[V]/[I]=1V/1A=1Ω (Ohm) ῤ is called a resistivity, [ ῤ ]=Ωm σ=1/ ῤ is called a conductivity

6. Volt-Amper characteristics Ohm’s Law: R is constant (characteristic of the conductor) It is valid for many conductors in a wide range of conditions, but not always! Semiconductor diode is a junction of two semiconductors with positive (p) and negative (n) carriers → p+p+ n-n- I + Change of a polarity of the battery results in zero current. It can be used for rectification of the current.

7. Thermal dependence of R In metals Hence if L(T),A(T) are negligible then Measuring R allows to find T (termistors) In semicoductors n~T→ ῤ ~1/T

9. Superconductors 10 Nobel prizes were given for studies of SC ;The last one in 2003 to theorists: Alexei Abrikosov, Vitaly Ginzburg, Anthony J. Legget 1911, Hg, T c ~4.2K, H.Kamerlingh Onnes, Nobel Prize in Physics in 1913 Up to 1986 T c <20K 1986, T c ~40K Karl Müller and Johannes Bednorz, Nobel Prize in Physics in 1987, Karl MüllerJohannes BednorzNobel Prize in Physics cuprate-perovskite ceramic materials, such as bismuth strontium calcium copper oxide (BSCCO) and yttrium barium copper oxide (YBCO); 1987, T c ~90K,….cuprateperovskiteceramicBSCCOYBCO 1993 T c ~135K still a record 2008 T c ~55K, Fe-based superconductors H.Kamerlingh Onnes,1853-1926 VitalyGinzburg, 1916-2009 Applications: electromagnets, motors, generators, transformers, etc. Open problems: 1.Mechanism of HTS? Why it’s possible? 2.How to sustain large current (high magnetic field) 3.Fragility of the materials Levitation

11. Resistors in series Resistors in parallel I3I3 I1I1 I2I2 NB: Opposite to capacitors! C=Q/V R=V/I

12. Example1.

13. Example 2

14. Electric Power ab I In resistor:

15. Alternative current (ac current)

16. How to get more light with two bulbs? Bulb B or ? Thomas Edison (1847-1931) 1882

17. How to get more light with two bulbs? Bulb B less light!more light!

18. emf, battery Closed loop loss of energy→ need a source of emf (ε), a battery I + emf (ε) is a work per unite charge by external (nonelectric force). Ideal case (neglecting losses in the battery): a b ε

19. ab ε r Terminal voltage and power output of the battery Terminal voltage is the voltage between the electrods of the battery connected to an external circuit, i.e. it is a voltage supplied by the battery to an external circuit. Real battery includes internal resistance, r. If the current through the battery is from – to + then the terminal voltage is smaller then emf:

20. Terminal voltage and power input into the battery If the current through the battery is from + to - then the terminal voltage is larger then emf: ab The rate at which the battery is charged The rate at which the battery is heated Alternator (the battery with larger emf delivers the energy to the battery with smaller emf

24. Ammeter measures the current. It should be placed in series with the element of circuit where it measures the current. Ideal ammeter has resistance=0 in order do not disturb in the current it measures. Voltmeter measure V. It should be placed in parallel with the element across which it measures the voltage. Ideal voltmeter has resistance=∞ in order do not disturb the voltage it measures. I I V =0 I

25. Simple resistors circuits 1.Open circuit. What ideal ammeter and voltmeter measure? A V I=0 (infinite resistance ) V=ε, P=0 r ε It’s dangerous to touch the ends! V=120V, R(wet body)=1kΩ→I~0.1A→ fibrillations (chaotic beatings of the heart) Defibrillator: I~1A complete stop