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Homework Help: The Black Box

  1. Aug 25, 2010 #1
    1. The problem statement, all variables and given/known data

    2 different types of components in a black box, which might be 2 of the following, resistor, capacitor or inductor.
    they can be in parallel or series.

    2 tests:

    1. DC voltage = 0.01 ohm

    2. fixed 1V AC RMS to the input and
    f=10Hz, I=75mA
    f=100Hz, I=20.9mA
    f=1kHz, I=19.6mA
    f=10kHz, I=19.5mA
    f=100kHz, I=19.5mA

    What are the 2 components? and are they in series or parallel? with reasoning, and the actual values of the components?



    2. Relevant equations



    3. The attempt at a solution

    I tried to plot z against w after a bit of calculation, i suspect they are LC in series or parallel.
    I can't get no further from that, even tho i have no idea it's right or wrong.

    Thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Aug 25, 2010
  2. jcsd
  3. Aug 25, 2010 #2

    Zryn

    User Avatar
    Gold Member

    Could you explain the first test?

    Did you calculate the resistance from a known DC voltage and a current measurement, or from a multimeter?

    What does a capacitor look like to a DC voltage? How about an inductor? You can rule out several combinations based on that knowledge.

    What does the reactance of a circuit look like as the frequency increases with a capacitor? How about an inductor?

    Are you able to put several DC voltages across the box and measure the current in test 1?

    How long did you wait before you took your measurement in test 2?
     
    Last edited: Aug 25, 2010
  4. Aug 25, 2010 #3
    I didn't do the experiment myself, it's a question from the paper.
    I typed it out exactly as it is on the paper.

    So i presume the DC resistance is measured

    'What does a capacitor look like to a DC voltage? How about an inductor? You can rule out several combinations based on that knowledge.'
    I don't quite get you here. Or i don't know

    'What does the reactance of a circuit look like as the frequency increases with a capacitor? How about an inductor?'
    I think a capacitor with Z against W, the graph looks like exp decay
    I think an inductor with Z against W, the graph looks like exp increase

    'Are you able to put several DC voltages across the box and measure the current in test 1?
    How long did you wait before you took your measurement in test 2?'
    No, only thing was given about the DC resistance was it's 0.01 Ohm
    and I presume the paper meant 'they' waited long enough to get a reading.

    Thanks
     
  5. Aug 25, 2010 #4
    there are 4 possibilities:
    L + R
    C + R
    L||R
    C||R

    first, at DC voltage (which produces a DC current), a capacitor becomes an open circuit. Since you observed a DC current, this eliminates C + R. Further, since an inductor becomes a short for DC voltage, you can eliminate R||L (otherwise, all current would flow down the short. You'd have, ideally, infinite current)

    So we can now have C||R or R + L. Since the impedance is increasing with frequency, the circuit must be an R + L. L's impedance is proportional to frequency, and a series combination would directly increase the overall impedance, lowering the overall current. C||R would have a decreasing capacitive impedance in parallel with some fixed R. As f increased, impedance would decrease.
     
  6. Aug 25, 2010 #5

    Zryn

    User Avatar
    Gold Member

    If you look at the base geometry principles for a capacitor, you will see that it is essentially two conducting plates separated by a dielectric material which will not conduct DC current under any circumstances (unless the capacitor is broken). This means that if you put a DC voltage across a capacitor you won't ever see current through it!

    By a similar token, the geometry of an inductor is essentially a long peice of wire, albeit with a special shape, that does nothing with a DC current through it (aside from the initial voltage change).

    So what happens if you have a capacitor in a DC series circuit? What about an inductor in a DC parallel circuit?

    Given a DC resistance of 0.01 Ohms, what do you think is happening?

    Reactance can be thought of as the AC resistance of a circuit.

    Are you familiar with Xl = jwL and Xc = 1/(jwC)? From these formula you can see that with an increasing frequency, the reactance will increase in one case, and decrease in the other. What happens in a DC circuit if you increase the resistance and keep the voltage steady? The same sort of things will happen in an AC circuit if you change the reactance (by changing the frequency) and keep the voltage steady.
     
  7. Aug 27, 2010 #6
    Thanks alot guys, you helped a great amount of deal.

    Calculating the resistance and the inductance
    I am abit unsure on how to calculate the inductance: Xl = jwL do i just ignore the imaginary j and assume it's just the value I need?

    Also do you guys happen to know filter designs?

    here is the question:
    Comment on factors, other than component tolerances, wiring resistance, inductance and capacitance, which would cause error between theoretical and practical cut-off frequency values, and make the designs less predictable.
     
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