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  • An electrical device draws 2kW power from AC mains (Voltage 223V(rms)=sqrt{50,000}v) The current differs (lags) in phase by phi (tan phi =frac{-3}{4}) as compared to voltage.

An electrical device draws 2kW power from AC mains  (Voltage\; 223V(rms)=\sqrt{50,000}v) The current differs (lags) in phase by  \phi \left ( \tan \phi =\frac{-3}{4} \right ) as compared to voltage. Find (i) R, (ii) XC – XL, and (iii) IM.

Answers (1)

Impedance,

Z=\sqrt{R^{2}+(X_{L}-X_{C})^{2}}=\sqrt{R^{2}+\left ( \omega L-\frac{1}{\omega C} \right )^{2}}

P=2000\; W

\tan \phi =-\frac{3}{4}

V_{rms}=223 \; V

P=\frac{V^{2}}{Z}

Z=25 \Omega

\frac{X_{c}-X_{L}}{R}=-\frac{3}{4}

X_{L}-X_{C}=-\frac{3}{4}R

R^{2}+(X_{L}-X_{C})^{2}=Z^{2}

R^{2}+\frac{9}{16}R^{2}=25^{2}

R^{2}=625*\frac{16}{25}=400

R=20 \Omega

X_{C}-X_{L}=-\frac{3}{4}*20=-15\Omega

I_{M}=\sqrt{2}I=\sqrt{2}\frac{V}{Z}=12.6 \; A

 

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