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29 April, 10:14

An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 46.8 H inductor, determine the inductive reactance and the rms current through the inductor. (a) the inductive reactance (in Ω)

(b) the rms current through the inductor (in A)

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  1. 29 April, 11:38
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    (a) 17634.24 Ω

    (b) 0.0068 A

    Explanation:

    (a)

    The formula for inductive inductance is given as

    X' = 2πFL ... Equation 1

    Where X' = inductive reactance, F = frequency, L = inductance

    Given: F = 60 Hz, L = 46.8 H, π = 3.14

    Substitute into equation 1

    X' = 2 (3.14) (60) (46.8)

    X' = 17634.24 Ω

    (b)

    From Ohm's law,

    Vrms = X'Irms

    Where Vrms = Rms Voltage, Irms = rms Current.

    make Irms the subject of the equation

    Irms = Vrms/X' ... Equation 2

    Given: Vrms = 120 V, X' = 17634.24 Ω

    Substitute into equation 2

    Irms = 120/17634.24

    Irms = 0.0068 A
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