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Complex currents and voltages - current in a branch

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  1. Oct 21, 2015 #1

    Rectifier

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    Gold Member

    The problem
    I want to calculate ## |I_1| ##

    RCMQMNp.jpg

    The attempt

    ## V_m = Z_{total}I_1 \\ I_1 = \frac{V_m}{Z_{total}} ##

    ## Z_{total} = \frac{ \frac{1}{jwC }\cdot (R + jwL) }{\frac{1}{jwC} + R + jwL} \\ \frac{ R + jwL }{1 + jwCR + jwCjwL} \\ \frac{ R + jwL }{1 - w^2LC + jwCR } \\ ##

    ## I_1 = \frac{V_m}{Z_{total}} = \frac{V_m}{\frac{ R + jwL }{1 - w^2LC + jwCR }} \\ = \frac{V_m(1 - w^2LC + jwCR)}{R + jwL} ##

    ## I_1 = \frac{V_m(1 - w^2LC + jwCR)}{R + jwL} \\ |I_1| = \frac{|V_m(1 - w^2LC + jwCR)|}{\sqrt{R^2 + (wL)^2}} ##

    This does not look right since the answer is ## \frac{R|V_m|}{R^2 + (wL)^2} ##

    Please help me.
     
  2. jcsd
  3. Oct 21, 2015 #2

    gneill

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    Staff: Mentor

    The given answer looks very suspicious since it doesn't include the capacitor impedance in any way. Your result looks okay to me.
     
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