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Mutual Inductance question regarding transformers. (AC electronics circuit theory)

  1. Nov 16, 2009 #1
    1. The problem statement, all variables and given/known data
    http://img265.imageshack.us/img265/8616/43354308.png [Broken]
    I have an exam coming up in a few days and I am doing some revision questions from some past exams and this is one I have attempted but I have no solutions to check my answers.

    3. The attempt at a solution
    using Vs = 12cos( 1000t - 90degrees)
    and w = 1000 I have transformed the circuit into their complex impedances

    Vs ~= 5.3 + 10i
    C1 = -4i
    L1 = 5i
    L2 = 6i
    LM = 3i
    R1 = 12


    a) Z22 = 6i+12

    b) (W^2 * M^2)/Z22 = Zr
    As W = 1000 and M = 3i
    Zr = 0.6 - 0.3i

    c) Zr + L1 + ZC = 0.6 + 1.3i

    d & e)
    Calculating the currents I1 and I2.

    Using these equations for the loops:
    Loop1: -vs + (Zc + L1)I1 - LM*I2 = 0
    Loop2: L2I2 + 12 - LMI1 = 0

    Loop1: I1 = -4i + 2I2
    Loop2 subbing I1 in I2 = 2 - 1.86i
    Hence I1 = 4 - 7.2i

    edit: I know I made a mistake with the algebra above but if I use KVL is that formula correct?

    Could someone verify that these answers are correct or that I am at least using the correct method?

    f)
    V = IR
    Vout = (2-1.86i)12
    Vout = 24 - 22.32i
    Vout = 32cos(1000t - 42degrees)

    g)Transformer has a step up effect as the magnitude of Vout is greater than that of Vs. Also, as the magnitude of I2 is less than that of I1 it seems logical to expect a greater voltage if the current is lower.
    32 > 12
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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