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15 September, 16:46

To find the reactance XLXLX_L of an inductor, imagine that a current I (t) = I0sin (ωt) I (t) = I0sin⁡ (ωt), is flowing through the inductor. What is the voltage V (t) V (t) V (t) across this inductor?

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  1. 15 September, 20:19
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    V (t) = XLI₀sin (π/2 - ωt)

    Explanation:

    According to Maxwell's equation which is expressed as;

    V (t) = dФ/dt ... (1)

    Magnetic flux Ф can also be expressed as;

    Ф = LI (t)

    Where

    L = inductance of the inductor

    I = current in Ampere

    We can therefore Express Maxwell equation as:

    V (t) = dLI (t) / dt ... (2)

    Since the inductance is constant then voltage remains

    V (t) = LdI (t) / dt

    In an AC circuit, the current is time varying and it is given in the form of

    I (t) = I₀sin (ωt)

    Substitutes the current I (t) into equation (2)

    Then the voltage across inductor will be expressed as

    V (t) = Ld (I₀sin (ωt)) / dt

    V (t) = LI₀ωcos (ωt)

    Where cos (ωt) = sin (π/2 - ωt)

    Then

    V (t) = ωLI₀sin (π/2 - ωt) ... (3)

    Because the voltage and current are out of phase with the phase difference of π/2 or 90°

    The inductive reactance XL = ωL

    Substitute ωL for XL in equation (3)

    Therefore, the voltage across inductor is can be expressed as;

    V (t) = XLI₀sin (π/2 - ωt)
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