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Homework Help: AC circuits - some questions

  1. May 4, 2008 #1
    1. The problem statement, all variables and given/known data
    In circuit given in attachment,find the value which is showed on ammeter A,if voltmeter is showing [tex]50\;V[/tex].

    Values are [tex]R=R_2=X_L=X_C=10\;\Omega[/tex] and [tex]R_1=5\;\Omega[/tex].

    3. The attempt at a solution
    First I calculate current thought branch with [tex]R_2[/tex] and [tex]X_C[/tex]:


    then knowing that potential difference at the ends of branches(one with [tex]R_2[/tex] and
    [tex]X_C[/tex] and the other with [tex]R_1[/tex] and [tex]X_L[/tex]) is the same,I proceed:




    Overall current [tex]\underline{I}[/tex] in circuit is the sum of two currents from two branches,so:


    Module of this value is value showed on ammeter:


    However,correct solution is:


    Where is the mistake?

    Attached Files:

    Last edited: May 4, 2008
  2. jcsd
  3. May 4, 2008 #2
    The second question is a theoretical one.Suppose that we have a simple system like one illustrated in attachment.

    If we need to find complex admittance of that system,we can write:


    from where we can see that it is [tex]B=\frac{-X_L}{R^2+X_L^2}[/tex],althought it is [tex]B=\frac{X_L}{R^2+X_L^2}[/tex].

    Why is this "-" just neglected,what is physical explanation of that?

    Or it is just hardcore mathematical laws against imperfect physical reality?

    Attached Files:

  4. May 5, 2008 #3
    OK,I managed to resolve first problem,but what about second one?
  5. May 5, 2008 #4
    Probably the explanation is that while one physical parameter is rising(susceptance [tex]B[/tex]),the other is lowering(inductive reactance [tex]X_L[/tex]) and vice-versa,like it is in Faraday`s law of induction:


    the magnetic field which is produced by induced current(which is in turn produced by induced electromotive force [tex]e[/tex]) is in oposition with the change of outer flux [tex]\phi[/tex](sorry if my technical english sounds a bit clumsy).

    But what if there is capacitor instead of inductor?
    In that case there is no confusion like this.
    Last edited: May 5, 2008
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