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24. Electric Current

24. Electric Current. Electric Current Conduction Mechanism Resistance & Ohm’s Law Electric Power Electrical Safety. How does electric current heat this light bulb filament? Where does the energy come from?. Collisions between e & ions. e accelerated by E. 24.1. Electric Current.

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24. Electric Current

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  1. 24. Electric Current Electric Current Conduction Mechanism Resistance & Ohm’s Law Electric Power Electrical Safety

  2. How does electric current heat this light bulb filament? Where does the energy come from? Collisions between e & ions. e accelerated by E.

  3. 24.1. Electric Current Current (I) = Net rate of (+) charge crossing an area. [ I ] = Ampere Electronics: I ~ mA Biomedics: I ~ A Steady current: Instantaneous current: + charges moving right Zero net current Net current  charges moving left Both charges moving right

  4. GOT IT? 24.1 • Which of the following representsa nonzero current? • What’s its direction? • a beam of electrons moves from left to right, • a beam of protons moves upward, • in a solution, positive ions move left & negative ions move right, • blood, carrying positive & negative ions at the same speed, moves up through a vein, • a metal car with no net charge speeds westward. I, R to L I, up I, L no I no I

  5. Curent: A Microscopic Look v of charge carriers in media with E = 0 isthermal ( random with  v  = 0 ). For E 0, vd =  v   0. drift velocity Charge in this volume is Q = n A L q. n = number of carriers per unit volume q = charge on each carrier

  6. Example 24.1. Copper Wire A 5.0-A current flows in a copper wire with cross-sectional area 1.0 mm2, carried by electrons with number density n = 1.11029 m3. Find the electron’s drift speed. TIP: Big difference between vd ~ mm/s and signal speed ~ c.

  7. Current Density Current can flow in ill-defined paths ( vd depends on position ), e.g., in Earth, chemical solutions, ionized gas, … Better description of such flows is by current density ( J ) = current per unit area [ J ] = A /m2   Charge density

  8. Example 24.2. Cell Membrane Ion channels are narrow pores that allow ions to pass through cell membranes. A particular channel has a circular cross section 0.15 nm in radius; it opens for 1 ms and passes 1.1104 singly ionized potassium ions. Find both the current & the current density in the channel. ~0.3 nm Lipid molecules ion channels ~ 4 times max. safe current density in household wirings AWG 10 :

  9. 24.2. Conduction Mechanism E 0 in conductor  non-electrostatic equilibrium  charges accelerated Collisions steady state   conductivity Ohm’s law, microscopic version Ohmic material:  independent of E   resistivity []  Vm/A  m []  (m)1

  10. No band gap Small band gap Large band gap

  11. Example 24.3. Household Wiring A 1.8-mm-diameter copper wires carries 15 A to a household appliance. Find E in the wire.

  12. GOT IT? 24.2 • Two wires carry the same current I. • Wire A has a larger diameter, • a higher density of current carrying electrons, • & a lower resistivity than wire B. • Rank order • the current densities, • the electric fields, • the drift speeds in the two wires. JA < JB EA < EB vA < vB

  13. Conduction in Metals Metal:  ~ 108  106 m Atomic structure: polycrystalline. Carriers: sea of “free” electrons, v ~ 106 m/s E = 0: equal # of e moving  directions   v = 0. E 0: Collisions between e-ph  vd~ const.  = relaxation time  Steady state: Ohm’s law Due to high T Bose statistics of phonons. Cu c.f., vth  T

  14. Ionic Solutions Electrolyte: Carriers = e + ions  ~ 104  105 m Examples: Ions through cell membranes. Electric eels. Batteries & fuel cells. Electroplating. Hydrolysis. Corrosion of metal.

  15. Plasmas Plasma: Ionized gas with e & ions as carriers. Examples: Fluorescent lamps. Plasma displays. Neon signs. Ionosphere. Flames. Lightning. Stars. Rarefied plasma (collisionless) can sustain large I with minimal E. E.g., solar corona.

  16. Thermal motion dislodges an e ... Semiconductor Pure semiC: T = 0, no mobile charge carriers. T  0, thermally excited carriers, e & holes.   increases with T … leaving a hole behind. Doped semiC: Mobile charge carriers from impurities. N-type: carriers = e. Impurities = Donors. E.g. P in Si. P-type: carriers = h. Impurities = Acceptors. E.g. B in Si. e & h move oppositely in E Phosphorous with 5 e Bound e jumps left, h moved to right P fits into Si lattice, leaving 1 free e

  17. PN Junction Current flows in only 1 direction Depletion region No battery: e & h diffuse across junction & recombine. Junction depleted of carriers. Reverse bias: e & h pulled away from junction. Depletion region widens. I ~ 0. Forward bias: e & h drawn to junction. Depletion region vanishes. I  0.

  18. Application: Transistor Large current change controlled by small signal (at gate): Amplifier, or Digital switch. Normally channel is closed ( I = 0 ) as one of the junctions is reverse biased. + V applied to gate attracts e to channel: I 0

  19. Superconductor Onnes (1911): Hg = 0 below 4.2K. Muller et al (1986): TC ~ 100K. Current record: TC ~ 160K. TC = Applications: Electromagnets for strong B: Labs, MRI, LHC, trains … SQUIDS for measuring weak B. YBaCuO

  20. 24.3. Resistance & Ohm’s Law Ohm’s Law macrscopic version Open circuit: R    I = 0  V Short circuit: R = 0  I    V   Resistor: piece of conductor made to have specific resistance. All heating elements are resistors. So are incandescent lightbulbs.

  21. Table 24.2. Micrscopic & Macroscopic Quantities in Ohm’s Law E V J I  R

  22. Example 24.4. Starting Your Car A copper wire 0.50 cm in diameter & 70 cm long connects your car’s battery to the starter motor. What’s the wire’s resistance? If the starter motor draws a current of 170A, what’s the potential difference across the wire?

  23. GOT IT? 24.3 • The figure shows 3 pieces of wire. • & (2) are made from the same material, while • (3) is made from material with twice the resistivity. • & (3) have twice the diameter of (2). • Which has the highest resistance? • If the same voltage is applied across each, • which will pass the highest current? (2) (1)

  24. 24.4. Electric Power Electric Power : for time independent V Power increase with R ( for fixed I ) Power decrease with R ( for fixed V ) No contradiction

  25. Conceptual Example 24.1. Electric Power Transmission Long distance power transmission lines operate at very high voltages – often hundreds of kVs. Why? Power P = I V. Transmission loss PW = I 2RW = P2RW / V2  Low I , i.e., high V , lowers PWfor same P. PW = (V  VL )2 / RW = (V  P RL / V )2 / RW see Prob 56 VL< V because of power loss in wire

  26. Making the Connection What is the current in a typical 120 V, 100 W lightbulb? What’s the bulb’s resistance?

  27. 24.5. Electrical Safety TABLE 24.3. Effects of Externally Applied Current on Humans Current Range Effect -------------------------------------------------------------------------------------------------- 0.5  2 mA Threshold of sensation 10  15 mA Involuntary muscle contractions; can’t let go 15  100 mA Severe shock; muscle control lost; breathing difficult 100  200 mA Fibrillation of heart; death within minutes > 200 mA Cardiac arrest; breathing stops; severe burns Typical human resistance ~ 105. Fatal current ~ 100 mA = 0.1 A.  A wet person can be electrocuted by 120V.

  28. Large current thru operator No current thru operator Large current blows fuse Ground fault interupter

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