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14 June, 09:00

A voltage of 12 cos (I000t+45) Vis applied to a circuit in which a resistor of 4. n, aninductor of L H, and a capacitor of 100 μF are connected in series. If the current in the circuit is in phase with the voltage, find the value of L

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  1. 14 June, 12:14
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    0.01 H

    Explanation:

    V = 12 cos (1000t + 45)

    C = 100 micro farad

    Let the inductance be L.

    When the current and the voltage are in the same phase so it is the condition of resonance.

    So capacitive reactance = inductive reactance

    Xc = XL

    1/ωC = ωL

    L = 1 / ω²C

    By comparisonV = Vo Cos (ωt + Ф)

    ω = 1000 rad/s

    L = 1 / (1000 x 1000 x 100 x 10^-6)

    L = 1 / 100

    L = 0.01H

    thus, the inductance of the inductor is 0.01 H.
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