lec18_021907_-_Currents_and_Resistors_III

lec18_021907_-_Currents_and_Resistors_III - Req, series = i...

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Unformatted text preview: Req, series = i Ri Kirchhoff's Rules Kirchhoff' I and R III 1 = Req, parallel i 1 Ri 4 =6V 2 Junction Rule: Derives from Conservation of Charge At any junction point in a circuit where the current can divide, the sum of the currents into the junction must equal the sum of the currents out of the junction! Loop Rule: Derives from Conservation of Energy When any closed-circuit loop is traversed, the sum of the closedchanges in potential must equal zero! 1 Find I and V through each resistor 3 Example Circuit 3 2 5 Sign Conventions Cross a battery from the negative terminal to the positive terminal: terminal: V is positive! Cross a resistor in the direction of positive current flow: V is negative! Cross from the negative plate of the capacitor to the positive plate of plate a capacitor: V is positive! And vice versa for all of the above! 1 Monday, 19 February 2007 2 Monday, 19 February 2007 Example Circuit Kirchhoff's Rules Kirchhoff' 2 R3 R2 R5 3 R4 Question If you increase the charge on a parallel-plate capacitor from parallel3 C to 12 C and decrease the plate separation from 4 mm to 1 mm, the energy stored in the capacitor changes by a mm, factor of ... A. 1/4 B. 12 C. 4 D. 1/12 E. 64 R1 1 Monday, 19 February 2007 3 Monday, 19 February 2007 4 1 Question A parallel-plate capacitor with a dielectric in the space in parallelbetween the plates has a capacitance of 8 F. Removing the dielectric and doubling the separation between the plates results in the capacitance becoming 2 F. What is the dielectric constant? Assume that the space between the plates is a vacuum once the dielectric is removed. A. 0.5 B. 2.0 C. 4.0 D. 0.25 E. 8.0 Monday, 19 February 2007 5 Question A fuse in an electric circuit is a wire that is designed to melt, melt, and thereby open the circuit, if the current exceeds a predetermined value. Suppose that the material composing the fuse melts once the current density rises to 500 A/cm2. What diameter of cylindrical wire should be used to limit the current to 0.2 A? A? A. 0.02 cm B. 2 10 -5 cm C. 0.04 cm D. 5 cm E. None of the above Monday, 19 February 2007 6 Question If the current in a resistor is doubled while the value of the resistance is cut in half, the power dissipated in that resistor is changed by a factor of ... A. 4 B. 2 C. D. 8 E. There is no increase or decrease in the power dissipated Question Light bulbs that have been on for a few seconds can be treated as resistors that glow more brightly when the power dissipated by their ohmic filaments is increase. Rank the identical light bulbs shown below according to brightness, from most to least bright. A. A > D > B > C B. A > B > D > C C. B = C > D > A D. A > D > B = C E. None of the above 7 Monday, 19 February 2007 8 A B D C Monday, 19 February 2007 2 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 Monday, 19 February 2007 9 Vo , capacitor = Vo , resistor f dQ dt = - Q (RC ) Qo o ln Qf Qo - =- (RC ) - tf tf Qo = Io R C Q Q Io = R o = C (RC ) Monday, 19 February 2007 Qf Qo =e - ( RC ) tf Q = Qo e ( RC ) tf = Qo e Where = RC is the time constant for the RC circuit 10 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! Monday, 19 February 2007 11 V f , resistor = 0 Qf = V f , capacitor = C Qf = C dQ I =+ dt Monday, 19 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 12 3 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 13 Monday, 19 February 2007 14 = I oe Monday, 19 February 2007 - t RC 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 15 0 A. B. C. D. (R1 + R2 ) R2 R1 16 0 E. None of the above Monday, 19 February 2007 E. None of the above Monday, 19 February 2007 4 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. A. B. C. D. (R1 + R2 ) R2 R1 17 0 A. B. CR2 (R1 + R2 ) C. C D. 0 CR1 (R1 + R2 ) E. None of the above Monday, 19 February 2007 E. None of the above Monday, 19 February 2007 18 5 ...
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