Unformatted text preview: Physics 212
Lecture 9
Today's Concept: Electric Current
Ohm’s Law & resistors, Resistors in circuits, Power in circuits
50 40 30 20 10 0 Confused Avg = 3.4 Confident Physics 212 Lecture 9, Slide 1 Music
Who is the Artist? A) B) C) D) E) Grateful Dead Jefferson Airplane CCR The Band ZZ Top Why? Last time I played Van Morrison tunes from this album Have you seen the movie? Best music movie ever?? 1978: Martin Scorcese 1978: Scorcese Clapton, Dylan. Dr. John, Joni Mitchell, Clapton, Van the Man, Neil Young, …
Physics 212 Lecture 9, Slide 2 Physics 212
Lecture 9
Today's Concept: Electric Current
Ohm’s Law & resistors, Resistors in circuits, Power in circuits
50 40 30 20 10 0 Confused Avg = 3.4 Confident Physics 212 Lecture 9, Slide 3 Some Exam Stuff
• Exam next Wednesday at 7:00
– – – – Covers material through lecture 8 Bring your ID: Rooms determined by discussion section (see link) Conflict exam at 5:15 – sign up in your gradebook if you need to If you have conflicts with both of these, you should have heard from Prof Errede about scheduling online.physics.uiuc.edu/courses/phys212/fall09/ExamPrepHe1.html Physics 212 Lecture 9, Slide 4 Thanks for your feedback about the course
There were, of course, a mixed bag of opinions on what would make the the course better. course However, here’s what I will take away from all the comments 1) Make sure we have time to devote to the problem for the day 2) Reduce the votes on preflight questions that most students got 3) Sorry.. The lecture notes were my best guess at what I would do.. Based on preflights, it is better for me to change the lecture to preflights it address what difficulties I see.. The real lecture slides are posted address osted on the web after the lecture…… on Physics 212 Lecture 9, Slide 5 Key Concepts:
1) How resistance depends on A, L, σ, ρ How 2) How to combine resistors in series and parallel 3) Understanding resistors in circuits Today’s Plan:
1) Review of resistance & preflights Review preflights 2) Work out a circuit problem in detail Physics 212 Lecture 9, Slide 6 I σ A L V
Observables: Conductivity – high for good conductors. Conductivity Ohm’s Law: J = σ E V = EL I = JA I/A = σV/L I/A I = V/R I = V/(L/σΑ)
R= L σA
Physics 212 Lecture 9, Slide 7 R = Resistance ρ = 1/σ This is just like plumbing!
I is like flow rate of water V is like pressure R is how hard it is for water to flow in a pipe is
To make R big, make L long or A small big, long L R= σA To make R small, make L short or A big To small, short Physics 212 Lecture 9, Slide 8 Preflight 2
Same current through Same both resistors both Compare voltages Compare across resistors across Preflight 4 70 60 50 40 30 20 10 0 L R∝ A
L V = IR ∝ A 70 60 50 40 30 20 10 0 A2 = 4 A1 ⇒ V2 = 1 V1 4 L2 = 2 L1 ⇒ V2 = 2V1
Physics 212 Lecture 9, Slide 9 Preflight 12 BB 60 I J≡ A
Same Current 50 J1 = J 3 = 2 J 2 40 30 20 1 J∝ A 10 0 Physics 212 Lecture 9, Slide 10 10 Resistor Summary
Series
R1 R2 R2 Each resistor on a different wire. Same for each resistor. Vtotal = V1 = V2 Different for each resistor Itotal = I1 + I2 Decreases 1/Req = 1/R1 + 1/R2
Physics 212 Lecture 9, Slide 11 11 Parallel
R1 Wiring Voltage Current Resistance Each resistor on the same wire. Different for each resistor. Vtotal = V1 + V2 Same for each resistor Itotal = I1 = I2 Increases Req = R1 + R2 Preflight 6 100 80 60 40 20 0 R2 in series with R3 Current through R2 and R3 is the same I 23 = V R2 + R3 Physics 212 Lecture 9, Slide 12 12 R1 = R2 = R3 = R Preflight 7
Compare the current through Compare R1 with the current through R2 I1/I2 = 1/2 I1/I2 = 1/3 I1/I2 = 1 I1/I2 = 2 I1/I2 = 3 Preflight 9
Compare the voltage Compare across R2 with the across with voltage across R3 voltage V2 > V3 V2 = V3 = V V2 = V3 < V V2 < V3 Preflight 10
Compare the voltage across Compare R1 with the voltage across R2 V1 = V2 = V V1 = ½ V2 = V V1 = 2V2 = V V1 = ½ V2 = 1/5 V 1/5 V1 = ½ V2 = ½ V
Physics 212 Lecture 9, Slide 13 13 60 50 40 30 20 10
R1 = R2 = R3 = R 0 Preflight 7
Compare the current through Compare R1 with the current through R2 I1/I2 = 1/2 I1/I2 = 1/3 I1/I2 = 1 I1/I2 = 2 I1/I2 = 3 We know: I 23 = V R2 + R3 I1 = I 23 V R1 Similarly: I1 = R2 + R3 R1 I1 R2 + R3 = =2 R1 I 23
Physics 212 Lecture 9, Slide 14 14 BB
60 50 40 30 R1 = R2 = R3 = R 20 10 0 Preflight 9
Compare the voltage Compare across R2 with the across with voltage across R3 voltage A B C D V2 > V3 V2 = V3 = V V2 = V3 < V V2 < V3 Consider loop V23 = V V23 = V2 + V3
R2 = R3 ⇒ V2 = V3
V V2 = V3 = 2 Physics 212 Lecture 9, Slide 15 15 BB
50 40 30 20 R1 = R2 = R3 = R 10 0 Preflight 10
Compare the voltage across Compare R1 with the voltage across R2 A V1 = V2 = V B C D E V1 = ½ V2 = V V1 = 2V2 = V V1 = ½ V2 = 1/5 V 1/5 V1 = ½ V2 = ½ V R1 in parallel with series in combination of R2 and R3 combination V 1= V23
R2 = R3 ⇒ V2 = V3
V1 = 2V2 = V
Physics 212 Lecture 9, Slide 16 16 V23 = V2 + V3 = 2V2 R1 V R2 Calculation
In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. R3 R4 What is V2, the voltage across R2? • Conceptual 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) Combine resistances to form equivalent resistances Evaluate voltages or currents from Ohm’s Law Expand circuit back using knowledge of voltages and currents • Strategic Analysis
– – – Physics 212 Lecture 9, Slide 17 17 R1 V R2 Calculation
In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω.
BB R3 R4 What is V2, the voltage across R2? • Combine Resistances:
R1 and R2 are connected: (A) in series (B) in parallel (B)
Parallel Combination Parallel
Ra (C) neither in series nor in parallel (C) Series Combination Series
Ra Rb Rb Parallel: Can make a loop that contains only those two resistors Series : Every loop with resistor 1 also has resistor 2.
Physics 212 Lecture 9, Slide 18 18 R1 V R2 Calculation
In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω.
BB R3 R4 What is V2, the voltage across R2? • Combine Resistances:
R2 and R4 are connected: (A) in series (B) in parallel (B) (C) neither in series nor in parallel (C) Series Combination Series
Ra Rb Series : Every loop with resistor 1 also has resistor 2.
Physics 212 Lecture 9, Slide 19 19 R1 V R2 Calculation
In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω.
BB R3 R4 What is V2, the voltage across R2? • Combine Resistances: R2 and R4 are connected in series = R24 = 2 + 4 = 6 Ω Redraw the circuit using the equivalent resistor R24 = series combination of R2 and R4.
R1 V R24
V R1 R3 R24 R1 V R3 R3 R24 (A) (A) (B) (C)
Physics 212 Lecture 9, Slide 20 20 R1 V Calculation
In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. R3 R24
BB R24 = 6Ω What is V2, the voltage across R2? • Combine Resistances:
What is the value of R234? R2 and R4 are connected in series = R24 R3 and R24 are connected in parallel = R234 (A) R234 = 1 Ω (A) (B) R234 = 2 Ω (B) (C) R234 = 4 Ω (C) (D) R234 = 6 Ω (D)
R234 = 2 Ω (1/Rparallel) = (1/Ra) + (1/Rb) 1/R234 = (1/3) + (1/6) = (3/6) Ω−1 Physics 212 Lecture 9, Slide 21 21 R1 V
I1 = I234 Calculation
In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. R234 R24 = 6Ω R234 = 2Ω What is V2, the voltage across R2? R1 and R234 are in series. R1234 = 1 + 2 = 3 Ω V
= I1234 R1234 Ohm’s Law tells us I1234 = V/R1234 = 18 / 3 = 6 Amps
Physics 212 Lecture 9, Slide 22 22 Calculation
V
I1234 R1234 In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω.
BB R24 = 6Ω R234 = 2Ω I1234 = 6 A What is V2, the voltage across R2?
R1 V
= I1 = I234 a I234 = I1234 Since R1 in series w/ R234 R234
b V234 = I234 R234 =6x2 = 12 Volts • What is Vab, the voltage across R234 ? (A) Vab = 1 V (B) Vab = 2 V (B) (C) Vab = 9 V (D) Vab = 12 V (C) (D) (E) Vab = 16 V (E) Physics 212 Lecture 9, Slide 23 23 Calculation
R1 V R234 V R1 R3 R24 V = 18V R 1 = 1Ω R2 = 2Ω R3 = 3Ω R4 = 4Ω. BB R24 = 6Ω R234 = 2Ω 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 Since R3 and R24 where combined in parallel to get R234 Voltages are same! Ohm’s Law I24 = V24 / R24 = 12 / 6 = 2 Amps
Physics 212 Lecture 9, Slide 24 24 Calculation
R1 V V R24 R1 R2 V = 18V R 1 = 1Ω R2 = 2Ω R3 = 3Ω R4 = 4Ω. BB R3 R3 R4 Which of the following are true? A) V24 = V2 B) I24 = I2 C) Both A+B D) None R24 = 6Ω R234 = 2Ω I1234 = 6 Amps I234 = 6 Amps V234 = 12V V24 = 12V I24 = 2 Amps What is V2? Since R2 and R4 where combined in series to get R24 Currents are same! Ohm’s Law V2 = I2 R2 = 2 x2 = 4 Volts!
Physics 212 Lecture 9, Slide 25 25 R1 V R2 Quick FollowUps
R1
a R3 R4 = V R234
b V = 18V R1 = 1Ω R2 = 2Ω R3 = 3Ω R4 = 4Ω. BB • What is I3 ? (A) I3 = 2 A (B) I3 = 3 A (B) (C) I3 = 4 A (C) R24 = 6Ω R234 = 2Ω V234= 12V V2 = 4V I1234 = 6 Amps V3 = Vab = 12V I3 = V3/R3 = 12V/3Ω = 4A • What is I1 ? We know I1 = I1234 = 6 A We
NOTE: I2 = V2/R2 = 4/2 = 2 A I1 = I2 + I3 Make Sense??? Physics 212 Lecture 9, Slide 26 26 ...
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 Fall '10
 Selig
 Current, Power, Resistor, Electrical resistance

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