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Numerical · Q26

Q.A resistor R=30 ΩR=30\ \Omega and an inductor L=0.1 HL=0.1\ \text{H} are connected in series to a 200 V200\ \text{V} (rms), 50 Hz50\ \text{Hz} AC source. Calculate

(a) the inductive reactance,
(b) the impedance of the circuit,
(c) the rms current, and
(d) the phase angle by which the current lags the voltage.
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Given: R=30 ΩR=30\ \Omega, L=0.1 HL=0.1\ \text{H}, Vrms=200 VV_{rms}=200\ \text{V}, f=50 Hzf=50\ \text{Hz}.

  1. Inductive reactance.

    XL=2π(50)(0.1)≈31.42 ΩX_L = 2\pi(50)(0.1) \approx 31.42\ \Omega

  2. Impedance.

    Z=R2+XL2=302+31.422=900+987.2=1887.2≈43.44 ΩZ = \sqrt{R^2+X_L^2} = \sqrt{30^2+31.42^2} = \sqrt{900+987.2} = \sqrt{1887.2} \approx 43.44\ \Omega

  3. RMS current.

    Irms=VrmsZ=20043.44≈4.60 AI_{rms} = \frac{V_{rms}}{Z} = \frac{200}{43.44} \approx 4.60\ \text{A}

  4. Phase angle. …
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