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10 October, 16:49

An RLC series circuit consists of a 50 Ω resistor, a 200 μF capacitor, and a 120-mH inductor whose coil has a resistance of 20 Ω. The source for the circuit has an rms emf of 240 V at a frequency of 60 Hz. Calculate the rms voltages across the inductor.

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  1. 10 October, 19:26
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    182.9 Volts

    Explanation:

    R = resistance of the resistor = 50 Ω

    C = capacitance of the capacitor = 200 μF = 200 x 10⁻⁶ F

    L = Inductance of the inductor = 120 mH = 0.12 H

    f = frequency = 60 Hz

    Capacitive reactance is given as

    X = (2πfC) ⁻¹

    X = (2 (3.14) (60) (200 x 10⁻⁶)) ⁻¹

    X = 13.3 Ω

    Inductive reactance is given as

    X' = 2πfL

    X' = 2 (3.14) (60) (0.12)

    X' = 45.2 Ω

    Impedance of the circuit is given as

    z = √ (R² + (X' - X) ²)

    z = √ (50² + (45.2 - 13.3) ²)

    z = 59.31 Ω

    V = rms emf of the source = 240 Volts

    rms voltage across the inductor is given as

    V' = V z⁻¹ X'

    V' = (240) (59.31) ⁻¹ (45.2)

    V' = 182.9 Volts
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