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Current and Circuits

AP Physics C: E&M. Current and Circuits. Introductory Terms. Current: Charge Flow. This is the drift of electrons due to a potential difference. AC: Alternating current. The polarity of the v oltage source switches back and forth causing charges in path to vibrate.

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Current and Circuits

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  1. AP Physics C: E&M Current and Circuits

  2. Introductory Terms Current: Charge Flow. This is the drift of electrons due to a potential difference. AC: Alternating current. The polarity of the voltage source switches back and forth causing charges in path to vibrate. DC: Direct current. A constantly applied voltage causes charged particles to drift in one direction Series: Elements in circuit are connected along one path. Parallel: Elements of circuits are connected on separate branches.

  3. Capacitors in a DC Circuit Adding capacitors in series will lower the capacitance of the circuit when compared to the possible capacitance of just one capacitor in the circuit. + - C1 Voltage source C2 C3 Only the first plate of the first capacitor and the last plate of the last capacitor are actually connected to the voltage source, so only these plates will gain or lose electrons due to the potential difference of the battery.

  4. Capacitors in a DC Circuit C1 Voltage source C2 + - C3 The inner plates are induced with charge. All capacitors carry an equivalent charge Q. The voltage across all elements in the series will add up to that of the battery. Each capacitor has a different capacitance and has the same charge, so the individual voltages will differ.

  5. Capacitors in a DC Circuit C1 Voltage source C2 + - C3 Q is the same for all so the equivalent capacitance can be found with: This should not be surprising since you are basically just making one big capacitor with a larger separation (d).

  6. Capacitors in a DC Circuit Adding capacitors in parallel will raise the capacitance of the circuit when compared to the possible capacitance of just one capacitor in the circuit. + - Voltage source C1 C2 C3 All capacitors are directly connected to the same voltage source so they will each reach the same potential difference when charged.

  7. Capacitors in a DC Circuit Voltage source C1 C2 C3 + - Since each capacitor may have a different capacitance, each may hold a different amount of charge, but the sum of the charge will equal that of one capacitor to replace those in parallel.

  8. Capacitors in a DC Circuit Voltage source C1 C2 C3 + - V is the same for all so the equivalent capacitance can be found with: This should not be surprising since you are basically just making one big capacitor with a larger surface area (A) for charge to be stored.

  9. Practice Problems #’s 8-12

  10. Circuit components + - + - + - + - + - + - + - A B D E C

  11. electric Current Electric current is the amount of charge passing through a certain area per second. It is measured in amperes. 1 C of charge through any cross section of wire per second is one AMP! It takes over 6.24 billion billion electrons to add up to one coulomb!

  12. Electric Current If the charge flow rate varies, we define the instantaneous current as: The direction of current is the direction that positive charges would flow if free to do so. n=number of charge carriers per unit volume A=cross-sectional area of wire Δx=length of section of wire ΔQ=charge in a section of wire q=charge on each particle

  13. Electric current If charge carriers move with a velocity vd, then they move a distance Δx=vdΔt

  14. Drift Velocity With no voltage, charges in a metal bounce around randomly similar to gas molecules. With a voltage they still bounce around but slowly drift in one direction.

  15. Drift Velocity A copper wire with cross-sectional area3x10-6m2 carries a current of 10.0A. Find the drift speed of the electrons. The density of copper is 8.95g/cm3. from the periodic table atomic mass of copper: m=63.5g/mol

  16. Drift Velocity A copper wire with cross-sectional area3x10-6m2 carries a current of 10.0A. Find the drift speed of the electrons. The density of copper is 8.95g/cm3.

  17. Then how do the lights come on so fast?

  18. We will define current density as: Current Density A current density J and an electric field E are established in a conductor when a potential difference is maintained across the conductor. The proportionality constant is called the conductivity of the conductor.

  19. Named after Georg Simon Ohm (1787-1854) Ohm’s Law For many materials, the ratio of the current density to the electric field is a constant, (sigma), that is independent of the electric field producing the current. This is not a law of nature, but an empirical relationship found to be valid for certain materials (most metals) If the potential difference is constant, the current is constant.

  20. Ohm’s Law For a segment of wire of length L: Resistance!

  21. The unit is the Ohm (Ω) Resistance The inverse of conductivity is resistivity!

  22. Resistance and Temperature: For all metals, resistivity increases with temperature increase. some reference value usually at 20°C Temperature coefficient of resistivity

  23. Electrical Energy and Power Divide both sides by time.

  24. Electrical Energy and Power

  25. Electromotive “Force” – (emf) An emf is any device (generator/battery) that produces an electric field and thus may cause charges to move around in a circuit. Is an emf (ε) any different than a voltage source (V)? Any real emf has a certain amount of its own internal resistance, so the voltage that it will supply to a circuit between terminals is slightly different than its own potential difference. Both are measured in Volts.

  26. Electromotive “Force” – (emf) An emf can be thought of as a charge pump. V is the terminal voltage Epsilon is the potential difference of the emf I is the circuit’s current r is the internal resistance of the emf R is the equivalent resistance of the circuit P is the power dissipated in circuit and emf device

  27. Kirchoff’s Rules for complex circuits: The sum of the currents entering any junction must equal the sum of the currents leaving that junction. The algebraic sum of the changes in potential across all of the elements around any closed loop must be zero. I am Bunsen. Have you tried my burner?

  28. Kirchoff’s Rules for complex circuits: Of course Bunsen, If charge is split between two branches it must flow down one path. it will not build up in a location or disappear. Also, a charge must gain as much energy as it loses throughout the circuit because it begins and ends at the same point. By the way, nice burner! Do you mean that Energy and Charge are conserved?

  29. RC Circuits What is different about a circuit with a resistor and a capacitor than one with just a resistor? + - The current does not flow at a constant rate! The charge stops flowing when a capacitor matches the battery voltage. It drains charge through the resistor after batter is disconnected. Why is this?

  30. At time t=0 the switch is closed and the full capacitor discharges. No current I ++++++ - - - - - - - - • +++ • - - - C R ΔVR=0 C R ΔVR=-IR ΔVC=Q0/C ΔVC=Q/C From the loop rule…

  31. Q and I are instantaneous values:

  32. Find the current expression for an RC circuit

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