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23 June, 23:29

Use phasor techniques to determine the impedance seen by the source given that R = 4 Ω, C = 12 μF, L = 6 mH and ω = 2000 rad/sec. Then determine the current supplied by the source given that V = 12 <0o v. The equivalent impedance seen by the source is Z = ∠ o Ω. (Round the magnitude to three decimal places and the angle to two decimal places.) The current supplied by the source is I = ∠ o A. (Round the magnitude to three decimal places and the angle to two decimal places.)

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  1. 23 June, 23:45
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    Z = 29.938Ω ∠22.04°

    I = 2.494A

    Explanation:

    Impedance Z is defined as the total opposition to the flow of current in an AC circuit. In an R-L-C AC circuit, Impedance is expressed as shown:

    Z² = R² + (Xl-Xc) ²

    Z = √R² + (Xl-Xc) ²

    R is the resistance = 4Ω

    Xl is the inductive reactance = ωL

    Xc is the capacitive reactance =

    1/ωc

    Given C = 12 μF, L = 6 mH and ω = 2000 rad/sec

    Xl = 2000*6*10^-3

    Xl = 12Ω

    Xc = 1/2000*12*10^-6

    Xc = 1/24000*10^-6

    Xc = 1/0.024

    Xc = 41.67Ω

    Z = √4² + (12-41.67) ²

    Z = √16+880.31

    Z = √896.31

    Z = 29.938Ω (to 3dp)

    θ = tan^-1 (Xl-Xc) / R

    θ = tan^-1 (12-41.67) / 12

    θ = tan^-1 (-29.67) / 12

    θ = tan^-1 - 2.47

    θ = - 67.96°

    θ = 90-67.96

    θ = 22.04° (to 2dp)

    To determine the current, we will use the relationship

    V = IZ

    I = V/Z

    Given V = 12V

    I = 29.93/12

    I = 2.494A (3dp)
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