worksheet on step-up and step-down transformers (Q21)

Discussion in 'General Electronics Chat' started by rdkirkden, Feb 9, 2015.

  1. rdkirkden

    Thread Starter New Member

    Feb 9, 2015
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    Re: http://www.allaboutcircuits.com/worksheets/trans1.html, Q21

    Q21 figure.pdf

    This represents an electric power system, with 10:1 step-up and step-down transformers connecting the voltage source, transmission line and load. The question says to calculate the voltage drop across the load, power dissipated by the load, power lost in the transmission line, and efficiency. Answers are given, but I am struggling with the workings!

    In particular, I'm having trouble with the current in the primary (voltage source) circuit. I think this should be affected by both the resistance of the load and the resistance of the transmission line. My workings are as follows.

    If the primary circuit is circuit 1, the line circuit is circuit 2 and the load circuit is circuit 3, then R21 is the resistance of circuit 2 as seen by circuit 1, R32 is the resistance of circuit 3 as seen by circuit 2, and R31 is the resistance of circuit 3 as seen by circuit 1.
    R21 = (turns ratio)^2 x actual resistance = (1/10)^2 x 0.2 =0.002 Ω
    R32 = 10^2 x 1.6 = 160 Ω
    R31 = (1/10)^2 x 10^2 x 1.6 = 1.6 Ω
    I3 = V3 / R3 = 240 / 1.6 = 150 A
    I2 = V2 / R32 = 2400 / 160 = 15 A
    I1 = V1 / (R21 + R31) = 240 / 1.602 = 149.813 A
    Hence, the simple series circuit that is equivalent to the above diagram has V = 240V, Rload = 1.6 Ω, Rline = 0.002 Ω, and I = 149.813 A

    However, this current gives me the wrong answer for power dissipated by the load:
    P = I^2 x R31 = (149.813)^2 x 1.6 = 35910 W,
    whereas the correct answer is 35.96 kW, suggesting that the current should in fact be 150 A.

    So it looks as if the current in the primary circuit is unaffected by the resistance of the transmission line. This does not make sense to me. Where am I going wrong?
     
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