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4 October, 22:30

The ac generator in a series RCL circuit has an rms voltage of 70.9 V. The values of the resistance, capacitive reactance, and inductive reactance are, respectively, R = 30.0 Ω, XC = 50.0 Ω, and XL = 90.0 Ω. What is the rms current in the circuit?

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Answers (2)
  1. 4 October, 23:05
    0
    1.418 A

    Explanation:

    From Alternating current,

    V = IZ ... Equation 1

    Where V = rms Voltage, I = rms current, Z = Impedance of the RLC circuit.

    make I the subject of the equation

    I = V/Z ... Equation 2

    But,

    Z = √[ (XL-Xc) ²+R²] ... Equation 3

    Where XL = inductive reactance, Xc = capacitive reactance, R = resistance

    Substitute equation 3 into equation 2

    I = V/√[ (XL-Xc) ²+R²] ... Equation 4

    Given: V = 70.9 V, XL = 90 Ω, Xc = 50 Ω, R = 30 Ω

    I = 70.9/√[ (90-50) ²+30²]

    I = 70.9/√ (40²+30²)

    I = 70.9/√ (1600+900)

    I = 70.9/√2500

    I = 70.9/50

    I = 1.418 A
  2. 5 October, 00:30
    0
    The RMS current in the circuit is 1.418 A

    Explanation:

    The equation of the impedance of an RCL circuit is equal to:

    Z = (R^2 + (XL - XC) ^2) ^1/2

    Z = (30^2 + (50-90) ^2) ^1/2 = 50 ohms

    To calculate the RMS current we must use Ohms' law, therefore:

    I = V/Z = 70.9/50 = 1.418 A
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