Test Question About Finding Time Constant with Dependent Source

Discussion in 'Homework Help' started by bluetooth tamer, Apr 29, 2015.

  1. bluetooth tamer

    Thread Starter New Member

    Jan 16, 2015
    23
    0
    Hi,

    I just got back a test from lecture last week where one of the questions asks to find the time constant when the circuit has a dependent voltage source of 0.5k*ix and 2 resistors each 2k Ohm. My answer is 40ms but it got marked wrong.

    Any help tackling this problem or showing me my error would be greatly appreciated.
    Here's the picture redrawn for clarity.

    Keep in mind that I make the assumption that this circuit is in DC steady state and this is not stated in the problem.

    My logic from the picture in text goes like this.
    The term ix = 0 because the cap is an open circuit. This makes the dependent source = 0, therefore the middle branch is a short and the resistance seen by the cap is 2k ohm. RC = 2k Ohm * 20 micro Farads.

    IMAG0237.jpg
     
  2. WBahn

    Moderator

    Mar 31, 2012
    17,777
    4,805
    Your problem is that you can't treat dependent sources like you do independent ones. When you are finding the Thevenin equivalent circuit seen by the capacitor, you have to recognize that the dependent source matters.
     
  3. bluetooth tamer

    Thread Starter New Member

    Jan 16, 2015
    23
    0
    Okay, I used Thevenin's equivalent and here's what I got:

    If I plug in a voltage source of 1V in place of the cap then I can do a KVL around the right loop.
    The equation I get is 1V = 2k*ix + 0.5k*ix where 1V/ix = 2.5k Ohms.
    Multiply this resistance with capacitance and the answer is 50ms.

    Is the correct way to approach such a problem?
     
  4. WBahn

    Moderator

    Mar 31, 2012
    17,777
    4,805
    Yep. Good job.

    Notice how the dependent voltage source completely masks the left hand resistor.
     
    bluetooth tamer likes this.
  5. bluetooth tamer

    Thread Starter New Member

    Jan 16, 2015
    23
    0
    That is an interesting tidbit that I won't be forgetting any time soon.
    Thank you for that nudge in the right direction.
    And I do want to express my gratitude in regards how All About Circuits welcomes and respects newbies asking questions as much as the next contributor.
     
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