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27 January, 01:07

Use phasor techniques to determine the current supplied by the source given that V = 6 <0o v, R = 7 Ω, C = 12 μF, L = 4 mH and ω = 2000 rad/sec. The current supplied by the source is I = ∠ ° A

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  1. 27 January, 02:41
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    Given Information:

    Voltage = V = 6 < 0° V

    Resistance = R = 7 Ω

    Capacitance = C = 12 μF

    Inductance = L = 4 mH

    Frequency = ω = 2000 rad/sec

    Required Information:

    Current = I = ?

    Answer:

    I = 0.174 <78.25° A

    Explanation:

    The current can be found using

    I = V/Z

    Where Z is the impedance an can be calculated as

    Z = R + J (XL - XC)

    Where XL is inductive reactance and XC is capacitive reactance

    XL = ω*L

    XL = 2000*0.004

    XL = 8 Ω

    XC = 1/ω*C

    XC = 1/2000*12x10⁻⁶

    XC = 41.66 Ω

    So the impedance can be calculated now

    Z = R + J (XL - XC)

    Z = 7 + J (8 - 41.66)

    Z = 7 - J33.66 Ω

    |Z| = √ (7²) + (-33.66) ²

    |Z| = 34.38 Ω

    Magnitude of the current

    I = V/|Z|

    I = 6/34.38

    I = 0.174 A

    Magnitude and angle both

    I = 6 < 0° / (7 - J33.66)

    I = 0.0355 + j0.1708 A

    in the polar form

    I = 0.174 <78.25° A
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