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Graph of current against time

  1. Jan 24, 2010 #1
    Hi, I need help with the last part. I have put each part with the answers.

    For b) ii) I want to know where does V=1.6 V come from?

    (a) A 2200 µF capacitor is charged to a potential difference of 12 V and then discharged through an electric motor. The motor lifts a 50 g mass through a height of 24 cm.

    (i) Show that the energy stored in the capacitor is approximately 0.16


    E = ½ CV^2 = 0.5 × 2200 × 10(–6) F × (12 V)^2
    E = 0.158 J

    (ii) What is the efficiency of the electric motor in this situation?

    E = mgh = 0.12 J
    Efficiency = 0.12 ÷ 0.16 J = 0.75

    (b) The capacitor is charged to 12 V again and then discharged through a 16  resistor.

    (i) Show that the time constant for this discharge is approximately 35 ms.


    t = RC = 35.2 s




    ---- I need help with ----


    (ii) Sketch a graph of current against time for this discharge on the grid below. You should indicate the current at t = 0 and t = 35 ms.

    Curve starting on I axis but not reaching t axis
    I = 1.6 V / 16Ohms = 100 mA shown on axis
    Curve passing through about 37 mA at t = 35 ms
     
  2. jcsd
  3. Jan 25, 2010 #2

    Andrew Mason

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    What is the equation for current as a function of time? Hint: it is the solution to the differential equation:

    [itex]V_C + V_R = 0[/itex] where [itex]V_R = IR = R(dQ/dt)[/itex] and [itex]V_C = Q/C[/itex]

    So:

    [tex]\dot Q + Q/RC = 0[/itex]

    AM
     
  4. Jan 25, 2010 #3
    Is there any other way, because this is precalculus physics?
     
  5. Jan 25, 2010 #4

    Andrew Mason

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    The solution is:

    [tex]Q = Q_0e^{-\frac{t}{RC}}[/tex]

    so:

    [tex]\dot Q = I = \frac{V}{R} = -\frac{Q_0}{RC}e^{-\frac{t}{RC}} = -\frac{V_0}{R}e^{-\frac{t}{RC}} [/tex]

    Can you graph that?

    AM
     
    Last edited: Jan 25, 2010
  6. Jan 26, 2010 #5
    Yeah, so at t=0, I = 12V/16ohms = 0.75A

    But the answer uses 1.6V, which I am not sure where they get from...

    "I = 1.6 V / 16 = 100 mA shown on axis "

    Shouldn't it be 12V since it says:

    "The capacitor is charged to 12 V again and then discharged through a 16ohms resistor"

    The time constant is approximately 35s, as the capacitance is 2200 microF.

    On the graph in the answer, they have Current = 37mA at t=35, and Current = 100mA at t=0?

    Basically, I cant get how they get the orignal V to be 1.6V, rather than 12V - there was no mention of 1.6V in the question...
     
  7. Jan 26, 2010 #6

    Andrew Mason

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    You are right. The answers given correspond to an initial voltage of 1.6 V, not 12. The correct answers are 750 mA and 277 mA.

    AM
     
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