Open-Response Homework Problem 9.1 For the figure to the right with R1 = 100?, R

Question

Open-Response Homework Problem 9.1 For the figure to the right with R1 = 100?, R2 = 200?, ?V0 = 10V , and C = 1000?F.

(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?

Open-Response Homework Problem 9.2 Consider the circuit below. All batteries have potential difference ?Vbatt. Use R1, R2, etc. for the resistances. Use the current directions drawn.

(a)List any series or parallel combinations of resistors. State whether the combinations you list are series or parallel combinations.

(b)Write a loop equation for loop 1 (ABCA).

(c)Write a loop equation for loop 2 (DACD).

(d)Write a junction equation for junction A.

Explanation / Answer

Question_(1)

As given in the question,

R1 = 100 , R2 = 200 , V0 = 10 V and C = 1000 F = 0.001 F

(a) The current through R1 immediately after S1 is closed,

I  = Imax  = V0 / R1  = 10 / 100 = 0.1 A

(b) For this circuit, the time constant:

T  = R1*C  = 100*(0.001) = 0.1 s

The current as a function of time, if S1 is closed at time t = 0,

  I  = Imax*[ 1 - e^-(t / T) ]  = 0.1*[ 1 - e^-(t / 0.1) ]

(c)   The current through R1 after S1 has been closed for a long time,

  I = 0 A

(d) The current through R2 immediately after S1 is opened and S2 is closed,

  I  =  Imax  =  V0 / R2 = 10 / 200 = 0.05 A

(e)   For this circuit, the time constant:

T  = R2*C  = 200*(0.001) = 0.2 s

The current as a function of time, if S2 is closed at time t = 0,

  I  = Imax*[ 1 - e^-(t / T) ]  = 0.05*[ 1 - e^-(t / 0.2) ]

Question_(2)

As given in the question: All batteries have potential difference Vbatt

(a) Series combination: R1 and R2 (suppose we denote this combination by R12)

Parallel combination: R12, R3 and R4

(b)   The loop equation for loop 1 (ABCA),

- Vbatt + I2*R3 - Vbatt - I3*R4 - Vbatt = 0

(c) The loop equation for loop 2 (DACD),

  - I1*R1 + Vbatt + Vbatt + I3*R4 - I1*R2 = 0

(d)   The junction equation for junction A,

I1 + I2 + I3  = 0

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