No credit will be given for answers without appropriate supporting work. Minimum

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No credit will be given for answers without appropriate supporting work. Minimum good presentation requires the following: (1) Symbolic expression for any formula, (2) Manipulation of symbolic expressions, not numeric expressions, (3) Substitution of numbers with units, (4) Reporting final answers with correct units and vector expressions, (5) Enough English description to allow the reader to have some idea what you are doing without looking at the math.

Open-Response Homework Problem 9.1 For the figure to the right with R1 = 100?, R2 = 200?, ?V0 = 10V , and C = 1000µF. (a)Initially, S1 is open and the capacitor is uncharged. Immediately after S1 is closed, what is the current through R1? (b)What is the current as a function of time, if S1 is closed at time t0 = 0? Define and give values for any constants you introduce. (c)After S1 has been closed for a long time, what is the current through R1? (d)After S1 has been closed for a long time, S1 is opened and S2 is closed. What is the current through R2 immediately after S2 is closed? (e)What is the current as a function of time, if S2 is closed at time t0 = 0?

Explanation / Answer

(a) at t=0, the capacitor acts as a short circuit with zero resistance. so current= V/R1=10/100 = 0.1 A

(b) i= ( V/R1)(1- e-t/R1C )

   R1c = time constant , V/R1= maximum current of current at t=0, c= 1000uF

(c) after a long time. which mean at t= infinity the capacitor gets fulls charged and blocks dc. it will act as an open circuit and hecnce cureent through R1 after a long time =0

(d) after a long time the voltage acroos capacitor= v= 10 volts. when switch s2 is closed,the capacitor starts discharging and current in R2 is given by i= V/R2 = 10/200 = 0.05 A

(e) i= ( V/R2) e-t/R2C

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