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Physics 212 Lecture 9

Physics 212 Lecture 9. Electric Current. Exam Here, Tuesday, June 26, 8 – 9:30 AM Will begin at 7:30 for those who must leave by 9. Office hours 1-7 PM, Rm 232 Loomis Bring your ID !. What Determines How They Move?. They move until E = 0 !. Spheres Cylinders Infinite Planes.

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Physics 212 Lecture 9

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  1. Physics 212 Lecture 9 Electric Current Exam Here, Tuesday, June 26, 8 – 9:30 AM Will begin at 7:30 for those who must leave by 9. Office hours 1-7 PM, Rm 232 Loomis Bring your ID !

  2. What Determines How They Move? They move until E = 0 ! Spheres Cylinders Infinite Planes Gauss’ Law Field Lines & Equipotentials Capacitor Networks Work Done By E Field Equipotentials Field Lines Series: (1/C23)=(1/C2)+(1/C3) Parallel C123 = C1 + C23 Change in Potential Energy Conductors Charges free to move E = 0 in conductor determines charge densities on surfaces 05

  3. Conductivity – high for good conductors. Ohm’s Law: J = s E Observables: V = EL I = JA I/A = sV/L I = V/(L/sA) R = Resistance r = 1/s I = V/R L R = sA I s A L V Note: “Conventional current flow”, I, is opposite to direction electrons flow

  4. To make R big, make L long or A small L R = To make R small, make L short or A big sA Analogy to flow of water I is like flow rate of water V is like pressure R is how hard it is for water to flow in a pipe

  5. Checkpoint 1a Checkpoint 1b Same current through both resistors Compare voltages across resistors

  6. Preflight 12 Same Current The SAME amount of current I passes through three different resistors. R2 has twice the cross-sectional area and the same length as R1, and R3 is three times as long as R1 but has the same cross-sectional area as R1. In which case is the CURRENT DENSITY through the resistor the smallest? A. Case 1 B. Case 2 C. Case 3

  7. Resistor Summary Series Parallel R1 R2 R1 R2 Each resistor on the same wire. Each resistor on a different wire. Wiring Different for each resistor. Vtotal = V1 + V2 Same for each resistor. Vtotal = V1 = V2 Voltage Same for each resistor Itotal = I1 = I2 Different for each resistor Itotal = I1 + I2 Current Increases Req = R1 + R2 Decreases 1/Req = 1/R1 + 1/R2 Resistance

  8. Three resistors are connected to a battery with emf V as shown. The resistances of the resistors are all the same, i.e. R1= R2 = R3 = R. Checkpoint 2a Current through R2 and R3 is the same Compare the current through R2 with the current through R3: A. I2 > I3 B. I2 = I3C. I2 < I3 R2 in series with R3

  9. I1 I23 We know: Similarly: R1 = R2 = R3 = R Checkpoint 2b Compare the current through R1 with the current through R2 A. I1/I2 = 1/2 B. I1/I2 = 1/3 C. I1/I2 = 1 D. I1/I2 = 2 E. I1/I2 = 3

  10. V2 V3 V23 Consider loop R1 = R2 = R3 = R Checkpoint 2c Compare the voltage across R2 with the voltage across R3 V2 > V3 A B V2 = V3 = V C V2 = V3 < V D V2 < V3

  11. V1 V23 R1 in parallel with series combination of R2 and R3 R1 = R2 = R3 = R Checkpoint 2d Compare the voltage across R1 with the voltage across R2 A V1 = V2 = V V1 = ½ V2 = V B C V1 = 2V2 = V D V1 = ½ V2 = 1/5 V V1 = ½ V2 = ½ V E

  12. Calculation R2 R1 In the circuit shown: V = 18V, R1 = 1W, R2 = 2W, R3 = 3W, andR4 = 4W. What is V2, the voltage across R2? V R3 R4 • Analysis: • Ohm’s Law: when current I flows through resistance R, the potential drop V is given by: V = IR. • Resistances are combined in series and parallel combinations • Rseries = Ra + Rb • (1/Rparallel) = (1/Ra) + (1/Rb)

  13. Calculation R1 and R2 are connected: (A) in series(B) in parallel(C) neither in series nor in parallel Parallel Combination Series Combination Series : Every loop with resistor 1 also has resistor 2. Parallel: Can make a loop that contains only those two resistors R2 R1 In the circuit shown: V = 18V, R1 = 1W, R2 = 2W, R3 = 3W, andR4 = 4W. What is V2, the voltage across R2? V R3 R4 • Combine Resistances:

  14. Calculation R2 R1 In the circuit shown: V = 18V, R1 = 1W, R2 = 2W, R3 = 3W, andR4 = 4W. What is V2, the voltage across R2? V R3 R4 • We first will combine resistances R2 + R3 + R4: • Which of the following is true? • R2, R3 and R4 are connected in series • R2, R3, and R4 are connected in parallel • R3 and R4 are connected in series (R34) which is connected in parallel with R2 • R2 and R4 are connected in series (R24) which is connected in parallel with R3 • R2 and R4 are connected in parallel (R24) which is connected in parallel with R3

  15. Calculation (A) (B) (C) R2 R1 In the circuit shown: V = 18V, R1 = 1W, R2 = 2W, R3 = 3W, andR4 = 4W. What is V2, the voltage across R2? V R3 R4 R2 and R4 are connected in series (R24) which is connected in parallel with R3 Redraw the circuit using the equivalent resistor R24 = series combination of R2 and R4.

  16. Calculation R1 V R3 R24 What is the value of R234? (A) R234= 1 W (B) R234= 2 W (C) R234= 4 W (D) R234= 6 W R234 = 2W 1/R234 = (1/3)+ (1/6) = (3/6) W-1 R24 = R2 + R4 = 2W + 4W = 6W In the circuit shown: V = 18V, R1 = 1W, R2 = 2W, R3 = 3W, andR4 = 4W. What is V2, the voltage across R2? • Combine Resistances: R2 and R4 are connected in series = R24 R3 and R24 are connected in parallel = R234 • R2 and R4 in series (1/Rparallel) = (1/Ra) + (1/Rb)

  17. Calculation R1 In the circuit shown: V = 18V, R1 = 1W, R2 = 2W, R3 = 3W, andR4 = 4W. R24 = 6W R234 = 2W What is V2, the voltage across R2? V I1 = I234 R234 R1 and R234 are in series. R1234 = 1 + 2 = 3 W Our next task is to calculate the total current in the circuit Ohm’s Law tells us I1234 = V/R1234 = 18 / 3 = 6 Amps V R1234 = I1234

  18. What is Vab, the voltage across R234 ? (A) Vab= 1 V (B) Vab= 2 V (C) Vab= 9 V (D) Vab= 12 V (E) Vab= 16 V V In the circuit shown: V = 18V, R1 = 1W, R2 = 2W, R3 = 3W, andR4 = 4W. R24 = 6W R234 = 2W I1234 = 6 A What is V2, the voltage across R2? I1234 R1234 R1 I234 = I1234 Since R1 in series w/ R234 a V R234 V234 = I234 R234 = 6 x 2 = 12 Volts = I1 = I234 b

  19. Calculation R1 R1 V V R3 R234 R24 R3 and R24 were combined in parallel to get R234 Voltages are same! V = 18V R1 = 1W R2 = 2W R3 = 3W R4 = 4W. R24 = 6W R234 = 2W I1234 = 6 Amps I234 = 6 Amps V234 = 12V What is V2? Which of the following are true? A) V234 = V24 B) I234 = I24 C) Both A+B D) None Ohm’s Law I24 = V24 / R24 = 12 / 6 = 2 Amps

  20. Calculation R2 R1 R1 I24 V V R3 R3 R24 R4 R2 and R4 where combined in series to get R24 Currents are same! Ohm’s Law V2 = I2 R2 = 2 x 2 = 4 Volts! The Problem Can Now Be Solved! V = 18V R1 = 1W R2 = 2W R3 = 3W R4 = 4W. R24 = 6W R234 = 2W I1234 = 6 Amps I234 = 6 Amps V234 = 12V V24 = 12V I24 = 2 Amps What is V2? I1234 Which of the following are true? A) V24 = V2 B) I24 = I2 C) Both A+B D) None

  21. Quick Follow-Ups R1 I1 I2 a I3 V R234 b • What is I3 ? (A) I3= 2 A (B) I3= 3 A (C) I3= 4 A I3 = V3/R3 = 12V/3W = 4A NOTE: I2 = V2/R2 = 4/2 = 2 A I1 = I2 + I3 Make Sense??? R2 R1 V = 18V R1 = 1W R2 = 2W R3 = 3W R4 = 4W. R24 = 6W R234 = 2W V234= 12V V2 = 4V I24 = 2 Amps I1234 = 6 Amps V = R3 R4 V3 = V234 = 12V • What is I1 ? We know I1 = I1234 = 6 A

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