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Lecture 07

Lecture 07. Current & Circuits October 11, 2005. Dis week …. Monday – finish resistance and current and begin electric circuit. There is a new WA on board. Friday – Quiz on Monday-Wednesday’s material NEXT FRIDAY – Examination #2 Studying is a good idea!. Last time. J and E.

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Lecture 07

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  1. Lecture 07 Current & Circuits October 11, 2005

  2. Dis week … • Monday – finish resistance and current and begin electric circuit. • There is a new WA on board. • Friday – Quiz on Monday-Wednesday’s material • NEXT FRIDAY – Examination #2 • Studying is a good idea!

  3. Last time ... J and E

  4. Consider a wire

  5. Micro-View “Resistivity” • depends on the material and is the mean time between collisions • ease of motion – mobility • resistance to motion - scattering

  6. + E L E C T R O N s V i - Power POWER Battery supplies energy to the resistor which, in turn, dissipates it in the form of heat. Work done on charge Q = Q x V REMEMBER: P=iV and P=i2R

  7. copper 12 volts 0 volts The figure below gives the electrical potential V(x) along a copper wire carrying a uniform current, from a point at higher potential (x=0m) to a point at a lower potential (x=3m). The wire has a radius of 2.45 mm. What is the current in the wire? What does the graph tell us?? *The length of the wire is 3 meters. *The potential difference across the wire is 12 m volts. *The wire is uniform. Let’s get rid of the mm radius and convert it to area in square meters: A=pr2 = 3.14159 x 2.452 x 10-6 m2 or A=1.9 x 10-5 m 2 Material is Copper so resistivity is (from table) = 1.69 x 10-8 ohm meters

  8. We have all we need….

  9. R1 R2 V1 V2 V i i Series Combinations

  10. R1, I1 R2, I2 V Parallel Combination??

  11. What’s This??? In Fig. 28-39, find the equivalent resistance between points (a) F and H and [2.5](b) F and G. [3.13] ?

  12. Moving on ….. Fun and Frolic With Electric Circuits

  13. V Power Source in a Circuit The ideal battery does work on charges moving them (inside) from a lower potential to one that is V higher.

  14. V By the way …. this is called a circuit! A REAL Power Sourceis NOT an ideal battery Internal Resistance EorEmf is an idealized device that does an amount of work E to move a unit charge from one side to another.

  15. A Physical Battery Internal Resistance

  16. Represents a charge in space Back to Potential Change in potential as one circuits this complete circuit is ZERO!

  17. Consider a “circuit”. This trip around the circuit is the same as a path through space. THE CHANGE IN POTENTIAL FROM “a” AROUND THE CIRCUIT AND BACK TO “a” is ZERO!!

  18. To remember • In a real circuit, we can neglect the resistance of the wires compared to the resistors. • We can therefore consider a wire in a circuit to be an equipotential – the change in potential over its length is slight compared to that in a resistor • A resistor allows current to flow from a high potential to a lower potential. • The energy needed to do this is supplied by the battery.

  19. NEW LAWS PASSED BY THIS SESSION OF THE FLORIDUH LEGISLATURE. • LOOP EQUATION • The sum of the voltage drops (or rises) as one completely travels through a circuit loop is zero. • Sometimes known as Kirchoff’s loop equation. • NODE EQUATION • The sum of the currents entering (or leaving) a node in a circuit is ZERO

  20. i R1 R2 V1 V2 V TWO resistors again

  21. A single “real” resistor can be modeledas follows: R b a V position ADD ENOUGH RESISTORS, MAKING THEM SMALLER AND YOU MODEL A CONTINUOUS VOLTAGE DROP.

  22. Consider voltage DROPS: -E +ir +iR = 0 or E=ir + iR rise Take a trip around this circuit.

  23. Circuit Reduction i=E/Req

  24. Multiple Batteries Watch the DIRECTION !!

  25. Reduction Computes i

  26. PARALLEL Another Reduction Example

  27. NOTICE ASSUMED DIRECTION OF TRAVEL Voltage Drops: -E1 –i1R1 + i2R2 + E2 +i1R1 = 0 From “a” -i3R1 + E2 – E2 –i2R2 =0 NODE I3 +i2 = i1

  28. In the figure, all the resistors have a resistance of 4.0 W and all the (ideal) batteries have an emf of 4.0 V. What is the current through resistor R?

  29. The Unthinkable …. Resistors and Capacitors in the same circuit?? Is this cruel or what??

  30. Initially, no current through the circuit Close switch at (a) and current begins to flow until the capacitor is fully charged. If capacitor is charged and switch is switched to (b) discharge will follow. RC Circuit How Fast ?

  31. What do you think will happen when we close the swutch? Close the Switch I need to use E for E Note RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)

  32. Really Close the Switch I need to use E for E Note RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)

  33. This is a differential equation. • To solve we need what is called a particular solution as well as a general solution. • We often do this by creative “guessing” and then matching the guess to reality. • You may or may not have studied this topic … but you WILL!

  34. Math !

  35. Time Constant

  36. Result q=CE(1-e-t/RC)

  37. q=CE(1-e-t/RC) and i=(CE/RC) e-t/RC

  38. Discharging a Capacitor qinitial=CE BIG SURPRISE! (Q=CV) i iR+q/C=0

  39. In Fig. (a), a R = 21, Ohma resistor is connected to a battery. Figure (b) shows the increase • of thermal energy Eth in the resistor as a function of time t. • What is the electric potential across the battery? (60) • If the resistance is doubled, what is the POWER dissipated by the circuit? (39) • Did you put your name on your paper? (1) Looking at the graph, we see that the resistor dissipates 0.5 mJ in one second. Therefore, the POWER =i2R=0.5 mW

  40. If the resistance is doubled what is the power dissipated by the circuit?

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