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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 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=Vsurface Drift velocity F v v0 t m if F 0 v v0 0 (though vrms ( v 2 ) ~ 105 m / s ) qE if F qE 0 v vd m is an average time between collisions typically vd vrms Drift velocity does depend on a sign of charges + ions in plasmas or electrolytes, holes in semiconductors Electrons in metals, - ions in plasmas, etc. Electric current is a flow of charges (charge transferred per unite time via a given cross section) dQ [Q] 1C I ; SI unite : [ I ] 1A ( Amper) dt [t ] 1s dQ qnAvd dt I qnAvd q 2 nA qE vd I E I E I m m I is in direction of vd of ch arg es 2 qi ni A i E If different types of carriers present: I mi i V I R Ohm’s Law: Georg Ohm (1787 - 1854). I E V q 2 nA E ;I V L mL V mL I where R 2 Resistance R q nA SI unite of R: [R]=[V]/[I]=1V/1A=1Ω (Ohm) I q 2 n J E; A m m 2 ;R q n J L A ῤ is called a resistivity, [ῤ]=Ωm σ=1/ῤ is called a conductivity E Volt-Amper characteristics V Ohm’s Law: I R 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 + I→ n - + Change of a polarity of the battery results in zero current. It can be used for rectification of the current. Thermal dependence of R In metals 1 ~ ~T T (invalid at lowT ) 0 [1 (T T0 )] L R A Hence if L(T),A(T) are negligible then R R0 [1 (T T0 )] Measuring R allows to find T (termistors) In semicoductors n~T→ῤ~1/T Superconductors 1911, Hg, Tc~4.2K , H.Kamerlingh Onnes , Nobel Prize in Physics in 1913 Up to 1986 Tc<20K 1986 , Tc~40K Karl Müller and Johannes H.Kamerlingh Bednorz, Nobel Prize in Physics in 1987 cuprate-perovskite ceramic materials, such Onnes,1853-1926 as bismuth strontium calcium copper oxide (BSCCO) and yttrium barium copper oxide (YBCO); 1987, Tc~90K,…. 1993 Tc~135K still a record 2008 Tc~55K, Fe-based superconductors 10 Nobel prizes were given for studies of SC ;The last one in 2003 to theorists: Alexei Abrikosov, Vitaly Ginzburg, Anthony J. Legget Levitation Applications: electromagnets, motors, generators, transformers, etc. Open problems: 1. 2. 3. Mechanism of HTS? Why it’s possible? How to sustain large current (high magnetic field) Fragility of the materials VitalyGinzburg, 1916-2009 Resistors in series Vab Vax Vxy Vyb Req R1 R2 R3 I I Resistors in parallel I1 I2 I3 I1 I 2 I 3 1 1 1 1 I Req Vab Vab R1 R2 R3 NB: Opposite to capacitors! C=Q/V R=V/I Example1. Example 2 Electric Power dWab Pin ; dWab Vab dq Pin Vab I dt If Vab 0 and I flows from a to b Pin 0 IfVab 0 but I flows from b to a Pin 0 Vab 0 a b I In resistor: Pout Pin 0 Pin Vab I 0 always! 2 V V IR Pin I 2 R R U Pt , 1kWhr 3.6 106 J Alternative current (ac current) V (t ) V0 cos t V0 I cos t I 0 cos t R 2 2 I 2 2 0 R P (t ) I 0 R cos t I rms R 2 2 I0 2 I rms I (t ) I 0 cos t 2 How to get more light with two bulbs? Thomas Edison (1847-1931) 1882 ? or Bulb B How to get more light with two bulbs? P I I R 2 P Req less light! R Bulb B Req 2 R 2 2 2 2R Req R / 2 2 2 2 P Req R / 2 R more light! 2 emf, battery Closed loop R0 loss of energy→ need a source of emf (ε), a battery ε a + b emf (ε) is a work per unite charge by external (nonelectric force). Ideal case (neglecting losses in the battery): Vab Pout Vab I I 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: a r ε b Vab Ir Pout Vab I Pout I I r 2 Terminal voltage and power input into the battery a b If the current through the battery is from + to - then the terminal voltage is larger then emf: Vab Ir Pout Vab I Pout I I r 2 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 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. IV=0 I I Simple resistors circuits 1.Open circuit. What ideal ammeter and voltmeter measure? ε r V A I=0 (infinite resistance ) V=ε, P=0 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