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Understanding Electric Current: Principles and Models in Physics for Scientists and Engineers II

This lecture from the Summer Semester of 2009 covers essential concepts of electric current, including definitions, charge carriers, and the pathways of electrons in conductive materials. It explores topics such as instantaneous and average current, drift speed in metals, Ohm's Law, and the microscopic model of current flow. Emphasis is given to the behavior of charges in different materials, the role of electric fields, and the implications of conductivity and superconductivity. This session is designed for physics students aiming to deepen their grasp of electrical phenomena.

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Understanding Electric Current: Principles and Models in Physics for Scientists and Engineers II

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  1. Lecture 8: June 8th 2009 Physics for Scientists and Engineers II Physics for Scientists and Engineers II , Summer Semester 2009

  2. Electric Current Electric current: A net flow of charges. + + + + + + Surface of area A, perpendicular to flow of charges Average current through A: SI units of current: Instantaneous current through A: Physics for Scientists and Engineers II , Summer Semester 2009

  3. Electric Current Direction Definition: The direction of the current is in the same direction as the flow of positive charge.  The direction of current is opposite to the direction in which negative charge flows. + + + + + + - - - - - - Physics for Scientists and Engineers II , Summer Semester 2009

  4. Charge Carriers Metals: Electrons are the charge carriers (negative charge flows). Electrolytes: Typically both positively and negatively charged ions contribute to the flow of charge. - - - - - - Physics for Scientists and Engineers II , Summer Semester 2009

  5. Electric Field in Conducting Wires Closed loop: • DV=constant in wire • E=0 inside the wire • Electrons do not move on average. Battery in the loop: • DV exists from one end of the • wire to the other end. • E inside the wire • Electrons move within the wire opposite to the electric field in the wire. • Electric current flows through the wire in the direction of electric field. (charge carriers are NOT in an electrostatic equilibrium). + - V=lower V=higher Physics for Scientists and Engineers II , Summer Semester 2009

  6. Microscopic Model of Current in a Metal Assumption: Charge carriers move with a drift speed vd. A q Only charge carriers that are in the gray cylinder will pass through cross sectional area A in a time interval Dt. The amount of charge in the gray cylinder is: Physics for Scientists and Engineers II , Summer Semester 2009

  7. Microscopic Model of Current in a Metal Average current in the conductor: Physics for Scientists and Engineers II , Summer Semester 2009

  8. Example: Drift Speed in a Copper Wire Assume: 12-gauge copper wire (A=3.31x10-6m2) Iavg=1.0 A (for running a typical light bulb) q = 1.60x10-19C (magnitude of the charge of an electron) Need: n (volume density of free electrons in copper) Physics for Scientists and Engineers II , Summer Semester 2009

  9. Example: Drift Speed in a Copper Wire 12-gauge copper wire (A=3.31x10-6m2) Iavg=1.0 A (for running a typical light bulb) q = 1.60x10-19C (magnitude of the charge of an electron) n=8.46x1028 1/m3 Assuming the current is always in the same direction, how long would it take an electron to drift through 5 m of wire? Physics for Scientists and Engineers II , Summer Semester 2009

  10. Current Density (current per unit area) “conductivity of the material” Physics for Scientists and Engineers II , Summer Semester 2009

  11. Ohm’s Law Rewritten Physics for Scientists and Engineers II , Summer Semester 2009

  12. A Model for Electrical Conduction (Paul Drude’s model in 1900) Drift speed approx. 10-4 m/s - Average speed between collisions: approx. 106m/s Physics for Scientists and Engineers II , Summer Semester 2009

  13. A Model for Electrical Conduction (Paul Drude’s model in 1900) Conductivity and resistivity in terms of microscopic quantities. Physics for Scientists and Engineers II , Summer Semester 2009

  14. Superconductivity R=0 for some materials below a critical temperature. (Useful in superconducting magnets  no permanent power supply necessary, but needs constant cooling) Physics for Scientists and Engineers II , Summer Semester 2009

  15. Electrical Power New circuit element: The resistor Potential Energy Change of Charge +q: c d Pot. energy increases for the charge, but chemical pot. energy in battery decreases. a b + - Pot. energy decreases for the charge. The potential energy is lost in collisions to the atoms in the resistor (the resistor heats up). Physics for Scientists and Engineers II , Summer Semester 2009

  16. Electrical Power As charge passes through resistor: Physics for Scientists and Engineers II , Summer Semester 2009

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