lec19_022107_-_RC_Circuit

lec19_022107_-_RC_Circuit - Big Picture 1. Electrostatics...

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Unformatted text preview: Big Picture 1. Electrostatics 2. Circuits Capacitors and Dielectrics: Storing Charge Current and Resistance Direct Current Circuits (Steady State and RC) At t = 0: 0: Q = Qo I = Io RC Circuit - Discharge t = 0: the time after the switch has been 0: thrown, after the E-field has been established Ein the circuit, when dQ/dt < > 0, but before any 0, charge has physically moved. Qo C I =- Qf Vo , capacitor = dQ Q = dt (RC ) t dQ dt =- (RC ) Q Vo , resistor = I o R 3. Magnetics 4. Optics Wednesday, 21 February 2007 1 Vo , capacitor = Vo , resistor f dQ dt = - Q (RC ) Qo o ln Qf Qo - =- (RC ) - tf tf Qo = Io R C Q 1 Qo Io = = R C (RC ) Wednesday, 21 February 2007 Qf Qo =e - ( RC ) tf Q = Qo e ( RC ) tf = Qo e Where = RC is the time constant for the RC circuit 2 RC Circuit - Discharge Q = Qo e I =- - RC Circuit - Charge Kirchhoff: At t = 0: 0: Vo , capacitor = 0 Q=0 I = Io Vo , resistor = I o R ( RC ) tf = Qo e - t - tf - IR - - 1 dQ = -Qo - e dt = Qo - e RC t I = I oe - t = Io R At t = : I =0 Io = Q dQ = R C dt 1 (C - Q )dt = RdQ C t Q =0 C C Q dQ - = R C C dt R Current can be derived from charge, so only the charge expressions are on the equation sheet! Wednesday, 21 February 2007 3 V f , resistor = 0 Qf = V f , capacitor = C Qf = C dQ I =+ dt Wednesday, 21 February 2007 dt dQ = RC C - Q 0 dt = RC Qf dQ C - Q 0 t C = ln RC C - Q t C e = C - Q 4 1 RC Circuit - Charge (C - Q ) e - e t t Question In the figure below, assume that the switch has been closed for a "long time." What is the smallest capacitor needed to time." maintain 90% of the original current through resistor R1 for 5 seconds after the switch has been opened? - t = - C e (C - Q ) C - Q t (C - Q ) = C e Current: I = - t Q = C 1 - e - t = Qf 1- e dQ dt t - 1 (- C )e RC =- RC A. C = - 5 s (R1 ln 0.9) B. C = - 5 s (R1 ln 0.1) C. C = R1 (5 s ) D. C = 0.9 R1 (5 s ) E. None of the above 5 Wednesday, 21 February 2007 I = Ioe C=- - t R1C ln =- I t =- Io RC t R ln(0.9) 6 = I oe Wednesday, 21 February 2007 - t RC t I R ln Io Question In the figure below, what is the current through C at t = 0? 0? Question In the figure below, what is the current through R2 at t = 0? 0? A. B. C. D. (R1 + R2 ) R2 C 7 0 A. B. C. D. (R1 + R2 ) R2 R1 8 0 E. None of the above Wednesday, 21 February 2007 E. None of the above Wednesday, 21 February 2007 2 Question In the figure below, what is the total current provided by the battery after a "long time"? Assume that the battery does not time" go dead. Question In the figure below, what is the maximum charge on the capacitor? Assume that the battery does not go dead. - I 2 R2 - VC = 0 VC = - I 2 R2 I 2 = (R1 + R2 ) A. B. C. D. (R1 + R2 ) R2 R1 9 0 A. B. CR2 (R1 + R2 ) C. C D. 0 Q = CVC = C - Q=C Q= (R1 + R2 ) R2 CR1 (R1 + R2 ) R1 + R2 - R2 (R1 + R2 ) E. None of the above Wednesday, 21 February 2007 E. None of the above Wednesday, 21 February 2007 CR1 (R1 + R2 ) 10 3 ...
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This note was uploaded on 04/08/2008 for the course PHGN 200 taught by Professor Japguy during the Fall '07 term at Mines.

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