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A/C circuits Pre-Lab questions

  1. Sep 13, 2015 #1
    1. The problem statement, all variables and given/known data
    For the RC circuit shown in Fig. 1, at some frequency the peak voltage across the capacitor and resistor are equal. Find the frequency at which this occurs. Show that the peak voltage across the capacitor or the resistor at this frequency is given by Vin/ √ 2. How would this compare if we had two resistors R instead of a resistor and a capacitor?

    fig 1. is an RC circuit with 1 capacitor (0.1μF), 1 resistor (1kΩ) and a voltage source.

    2. Relevant equations
    1. Zc = −i/ ωC
    2. |Zc| = |Vc|/ |I| = 1/ ωC ,
    3. R = V/I
    4. ω=2πf
    3. The attempt at a solution

    To be honest it's been a very long time since I've done any physics and I'm having a little difficulty re-learning all the circuit stuff.

    To get the frequency the only thing I can think of is setting Vc equal to V to get

    IR=I/wC=I/2πfC

    Then,

    f=1/2πCR

    so,

    f=1/2π(0.1μF)(1kΩ)=1591.55Hz

    As for the next part, I'm really not sure what it is asking. Perhaps if I knew exactly what Vin/ √ 2 is then I'd be able to make some progress.

    But using the formulas, the peak voltage across the capacitor is

    |Vc|/ |I| = 1/ ωC (I think)

    And I don't know a formula for the peak voltage across the resistor, the only formula I have for the resistor is

    R = V/I


    And actually another thing I am confused about is the difference between resistance and impedance because it seems they use these terms interchangeably.


    Thanks guys.
     
  2. jcsd
  3. Sep 13, 2015 #2

    Simon Bridge

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    Is this a series or parallel circuit?
    If V is the voltage across the resistor, then putting Vc=V is just what the description says.
    Your reasoning looks long winded: if ##V_c=V## then ##Z_c=##?

    The next part is asking you to rewrite your equation for the frequency in terms of the input voltage. Clearly the frequency cannot be the (scaled) input voltage since they don't have the same units.

    Impedence is resistance that depends on frequency... so, at a constant frequency, they are the same thing.
     
  4. Sep 14, 2015 #3
    This is a series circuit.

    So what I have so far is that we are trying to find the frequency when |VR|=|VC|

    |VR|=IR
    |VC=I(1/wC)

    IR=I(1/wC), w=2πf

    Rearrange to get
    f=1/(2πCR), or w=1/(CR)

    Now to show that the peak voltage for the cap and the resistor at this frequency can be written as Vin/√2

    I can take the ratio |VC|/|Vin|= (1/wC)/(R2+(1/wC)2)1/2

    and so
    |VC|/|Vin|=1/ (1+(wCR)2)1/2

    plug in w=1/(CR) (from before)

    and I get

    |VC|/|Vin|=1/ (1+(CR/CR)2)1/2=|VC|/|Vin|=1/ (1+(1)2)1/2=1/√2

    thus |VC|=|Vin|/√2
     
  5. Sep 18, 2015 #4

    Simon Bridge

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    Well done.
     
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