Prozorov_09 - PHYSICS 222 Introduction to Classical Physics...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURE 9 RC circuits Power distribution an RC circuit as the name implies, it is a circuit with resistors and capacitors. The simplest one: R C ε PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 2 Charging the capacitor R Capacitor initially uncharged. At t = 0, close the switch. t = 0+ : (right after) ε C –+ – + Q (0) 0 I (0) R Current flows “through” C as through an ideal wire PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 3 R Charge builds up on the capacitor’s plates, and Q (t ) VC (t ) C EC (t) Ebattery +++ ––– ε C Adding charge to the plates is more and more difficult. After a long time, VC and charges cannot move. At t ∞ : Q () C I () 0 C acts like an open switch PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 4 charging, discharging and timing … PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 5 When the capacitor is fully charged and behaves like an open switch, there is still current in this circuit! I R1 R2 R1 R2 A C I B The potential difference between points A and B is: VA VB IR1 IR2 R2 Q CVC CIR2 C C R1 R2 PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 6 charging the capacitor (quantitative) Kirchhoff’s loop equation at t : IR I R Q 0 C dQ dt C ε dQ Q R 0 dt C Q (t ) C 1 e t Q (0) 0 RC Time constant + PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 7 Q (t ) C 1 e t d dt C t I (t ) e C C RC R Q Cε I t t I (t ) e R R PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 t 8 what is “time constant” τ? I ( ) I (0)e 1 0.37 I (0) When t = , (37% of I0) indicates how fast the current/charge are changing. I I(0) > Short ↔ Fast decay Long ↔ Slow decay t t means PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University t DEMO: Charge through bulb. 12 September 2011 9 which one is faster? In the two circuits below, the capacitors are identical, but the resistors and the batteries are not. 2R R C 24 V C 12 V Circuit 2 Circuit 1 When the switches are closed, the current in circuit 1 decays _________ than in circuit 2. A. Faster B. Slower PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University C. At the same rate 12 September 2011 10 = RC = 2RC Slower decay 2R R C 24 V C 12 V Circuit 1 Circuit 2 The battery does not make a difference in time. It affects the final charge in the capacitor and the magnitude of the initial current (both larger in circuit 1) PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 11 current decay How long after the switch is closed will the current be a quarter of its maximum value? 1 kΩ 10 mF 2 kΩ 12 V Maximum current I0 right after closing switch. For t 0, I I0 exp t I I0 4 with 3 k (10 mF) 30 s 1 exp t 4 PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University Req t ln 4 42 s 12 September 2011 12 discharging a capacitor R The capacitor has an initial charge Q0 . At t = 0, close the switch. C Q0 t = 0+ : (right after) Q (0) Q0 VC C Q0 I (0) R R RC Capacitor is a “battery” and supplies voltage Q/C PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 13 Q decreases R C VC decreases I decreases At t ∞ : Q () 0 PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University I () 0 12 September 2011 14 discharging the capacitor (quantitative) Kirchhoff’s loop equation at t : R Q IR 0 C I dQ dt C (Q is decreasing but we want I > 0) dQ Q 0 dt RC + Q (0) Q0 PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University Q (t ) Q0e t RC Time constant 12 September 2011 15 time constant The capacitor in the circuit is charged when the switch is at A. It is left at A for long time. Then, it is moved to B and the capacitor is discharged. What is the time constant for this process? R A B A. = RC R C B. = 2RC PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University C. = RC/2 12 September 2011 16 The formula = RC is for a capacitor and a resistor in series. R R C R reshape R Req = R/2 C PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 17 power distribution systems—a home • Potential, resistors, outlets, input from the power company … no wonder electricians are integral contractors in home construction! PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 18 fuses, circuit breakers, and GFI o A fuse will melt and a breaker will open the circuit if maximum current is reached. o A ground fault interrupter (GFI) stops further current flow when a sudden drop in resistance indicates that something provided a new easier path to current flow. PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 19 the wiring diagram for a typical kitchen PHYS222 - Lecture 9 - Prof. Ruslan Prozorov - Iowa State University 12 September 2011 20 ...
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This note was uploaded on 11/14/2011 for the course PHYS 5863005 taught by Professor Meyer during the Fall '09 term at Iowa State.

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