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Chapter 19

Chapter 19. A Microscopic View of Electric Circuits. Current in a Circuit. A microscopic view of electric circuits: Are charges used up in a circuit? How is it possible to create and maintain a nonzero electric field inside a wire? What is the role of the battery in a circuit?.

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Chapter 19

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  1. Chapter 19 A Microscopic View of Electric Circuits

  2. Current in a Circuit • A microscopic view of electric circuits: • Are charges used up in a circuit? • How is it possible to create and maintain a nonzero electric field inside a wire? • What is the role of the battery in a circuit? In an electric circuit the system does not reach equilibrium! Steady state and static equilibrium • Static equilibrium: • no charges are moving • Steady state (Dynamic Equilibrium): • charges are moving • their velocities at any location do not change with time • no change in the deposits of excess charge anywhere

  3. Current in Different Parts of a Circuit IB = IA in a steady state circuit We cannot get something for nothing! What is used up in the light bulb? Energy is transformed from one form to another Electric field – accelerates electron Friction – energy is lost to heat Battery – chemical energy is used up Closed circuit – energy losses to heat: not an isolated system!

  4. The Drude Model E - average time between collisions Momentum principle: Speed of the electron: Average ‘drift’ speed:

  5. The Drude Model - average time between collisions Paul Drude (1863 - 1906) Average ‘drift’ speed: For constant temperature u – mobility of an electron Electron current:

  6. E and Drift Speed Ethick Ethin i i In steady state current is the same everywhere in a series circuit. What is the drift speed? Note: density of electrons n cannot change if same metal What is E?

  7. Question 1.5.n1 = n2 2.u1 = u2 1018 1 mm 2 mm Every second 1018 electrons enter the thick wire. How many electrons exit from the thin wire every second? C) 2 x 1018 D) 4 x 1018 E) 12 x 1018 1018 1.5 x 1018

  8. Question 1.5.n1 = n2 2.u1 = u2 1018 1 mm 2 mm What is the ratio of the electric field, E1/E2? 3:1 6:1 8:1 12:1

  9. Direction of Electric Field in a Wire E must be parallel to the wire E is the same along the wire Does current fill the wire? Is E uniform across the wire? VAB 0 VCD 0

  10. Connecting a Circuit When making the final connection in a circuit, feedback forces a rapid rearrangement of the surface charges leading to the steady state. This period of adjustment before establishing the steady state is called the initial transient. The initial transient

  11. Connecting a Circuit • Static equilibrium: nothing moving • (no current) • Initial transient: short-time process • leading to the steady state 3. Steady state: constant current (nonzero)

  12. Current at a Node Gustav Robert Kirchhoff (1824 - 1887) i1 = i2 i2 = i3 + i4 The current node rule (Kirchhoff node or junction rule [law #1]): In the steady state, the electron current entering a node in a circuit is equal to the electron current leaving that node (consequence of conservation of charge)

  13. Exercise Write the node equation for this circuit. What is the value of I2? I1 + I4 = I2 + I3 I2 = I1 + I4 - I3 = 3A What is the value of I2if I4 is 1A? I1 + I4 = I2 + I3 I2 = I1 + I4 - I3 = -2A Charge conservation: 1A Ii > 0 for incoming Ii < 0 for outgoing

  14. Energy in a Circuit Vwire = EL Vbattery = ? Energy conservation (the Kirchhoff loop rule [2nd law]): V1 + V2 + V3 + … = 0 along any closed path in a circuit V= U/q  energy per unit charge

  15. Potential Difference Across the Battery FC EC Coulomb force on each e non-Coulomb force on each e 1. FC =eEC 2. FC =FNC Fully charged battery. Energy input per unit charge emf– electromotive force The function of a battery is to produce and maintain a charge separation. The emf is measured in Volts, but it is not a potential difference! The emf is the energy input per unit charge. chemical, nuclear, gravitational…

  16. Field and Current in a Simple Circuit Round-trip potential difference: We will neglect the battery’s internal resistance for the time being.

  17. Field and Current in a Simple Circuit Round-trip potential difference: Path 1 Path 2

  18. V Across Connecting Wires The number or length of the connecting wires has little effect on the amount of current in the circuit. uwires>> ufilament Work done by a battery goes mostly into energy dissipation in the bulb (heat).

  19. Twice the Length Nichrome wire (resistive) Current is halved when increasing the length of the wire by a factor of 2.

  20. Doubling the Cross-Sectional Area Loop:emf - EL = 0 Electron current in the wire increases by a factor of two if the cross-sectional area of the wire doubles. Nichrome wire

  21. Two Identical Light Bulbs in Series Two identical light bulbs in series are the same as one light bulb with twice as long a filament. Identical light bulbs The filament lengths add …

  22. Two Light Bulbs in Parallel L … length of bulb filament 1. Path ABDFA: 2. Path ACDFA: F iB = iC ibatt = 2iB 3. Path ABDCA: We can think of the two bulbs in parallel as equivalent to increasing the cross-sectional area of one of the bulb filaments. The filament areas add …

  23. Analysis of Circuits The current node rule (Charge conservation) Kirchhoff node or junction rule [1st law]: In the steady state, the electron current entering a node in a circuit is equal to the electron current leaving that node Electron current:i = nAuE Conventional current:I = |q|nAuE The loop rule (Energy conservation) Kirchhoff loop rule [2nd law]: V1 + V2 + V3 + … = 0 along any closed path in a circuit V= U/q  energy per unit charge

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