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DC Circuits

DC Circuits. Electromotive Force Resistor Circuits Connections in parallel and series Kirchoff’s Rules Complex circuits made easy RC Circuits Charging and discharging. Kirchoff’s Laws. Branch Theorem Loop Theorem. Electromotive Force (EMF).

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DC Circuits

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  1. DC Circuits • Electromotive Force • Resistor Circuits • Connections in parallel and series • Kirchoff’s Rules • Complex circuits made easy • RC Circuits • Charging and discharging

  2. Kirchoff’s Laws • Branch Theorem • Loop Theorem

  3. Electromotive Force (EMF) EMF, E, is the work per unit charge done by a field such as a battery or generator. Ideally, E=DV But every real life source has internal resistance, r If I=0 then DV=E

  4. Resistors in Series In a series connection, the current through one resistor is the same as the other, the potential drop on each resistor adds up to the applied potential.

  5. Resistors in Parallel In a parallel connection, the voltage across the resistors are the same, current gets divided at the junctions.

  6. Concept Question Charge flows through a light bulb. Suppose a wire is connected across the bulb as shown. When the wire is connected, • all the charge continues to flow through the bulb. • half the charge flows through the wire, the other half continues through the bulb. • all the charge flows through the wire. • none of the above

  7. Concept Question The light bulbs in the circuit are identical. When the switch is closed, • both go out. • the intensity of light bulb A increases. • the intensity of light bulb A decreases. • the intensity of light bulb B increases. • the intensity of light bulb B decreases. • some combination of 1–5 occurs. • nothing changes.

  8. Finding Req by Symmetry Since the circuit is symmetric on the a-c and a-d paths… The current through each should be equal Then the potential drop on those resistors will also be the same Then no current flows through the 5W resistor. It can be removed and points c and d can be connected

  9. More Complicated Circuits Not really possible to reduce to a single loop with an equivalent resistance

  10. Iout1 Iin DV+DV+DV=0 Iout2 Kirchoff’s Rules Revisited • The sum of currents entering a junction is equal to the sum of currents leaving it. • The sum of potential differences across all elements around a closed loop is zero.

  11. Sign Conventions • The potential change across a resistor is -IR if the loop is traversed along the chosen direction of current (potential drops across a resistor). • The potential change across a resistor is +IR if the loop is traversed opposite the chosen direction of current. • If an emf source is traversed in the direction of the emf, the change in potential is +E. • If an emf source is traversed opposite the direction of the emf, the change in potential is -E.

  12. Announcements • Cell phones on silent • Error in figure for question 1 in Reading Quiz 11.

  13. R2 R1 I1 I2 I3 V2 V1 R3 R4 R5 Using Kirchoff’s Rules Draw a circuit diagram and label all known and unknown quantities. Assign currents to each branch. Don’t worry about direction, but be consistent. Apply the junction rule to any junction in the circuit that provides a relationship between the various currents. Apply the loop rule to as many loops in the circuit as necessary to solve for the unknowns. Follow the sign rules. Solve the equations simultaneously.

  14. Example 28.9 (abcda) (befcb)

  15. House wiring: Lights, switches, fuses • One switch, multiple lights. • Two switches, multiple lights. • Three switches, multiple lights. • 324 switches, multiple lights.

  16. RC Circuits t = 0 t < 0 I = 0, q = 0 t > 0 q = Q

  17. Charging a Capacitor t = RC

  18. Example 28.12 t= ? Q = ? Imax = ? I(t) = ? q(t) = ? E= 12 V C = 5 mF R = 8x105W

  19. Discharging a Capacitor q=Q, I=0

  20. Example 28.13 (a) (b)

  21. Time Constants • Time constants are common in science! Given a time constant, t, how long does one have to wait for something to decay by: 10% .105t 25% .288t 50% .693t 90% 2.30t 99% 4.60t 99.99% 9.21t

  22. Ammeters and Voltmeters An ideal ammeter should have no resistance. In practice, its resistance should be very low compared to the circuit it is attached to. An ideal voltmeter should have infinite resistance. In practice, its resistance should be very high compared to the element it is attached to.

  23. Summary • EMF device as a charge pump • Power and energy in circuits • Loop and junction rules • Resistors in series and parallel • RC Circuits

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