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Average power in ac circuit and power factor - class-XII
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An electrical device draws 2 kW power from ac mains voltage 223 V(rms). The current differs lags in phase by $\phi = tan^{-1} \left ( -\frac{3}{4} \right )$ as compared to voltage. The resistance R in the circuit is:
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A
20 $\Omega$
💡 Explanation:
Here, $P , = , 2 , kW , = , 2 , \times , 10^3W$
$V _{rms} , = , 233 , V, tan , \phi , = , -\dfrac{3}{4}$
$As, , P , = , \dfrac{V^2 _{rms}}{Z}$
$\Rightarrow , Z , = , \dfrac{V^2 _{rms}}{P} , = , \dfrac{(223)^2}{2000} , = \dfrac{49729}{2000} , = , 24.86 , \Omega , or , Z , = , 25 , \Omega$
$\tan , \phi , = , \dfrac{X _C , - , X _L}{R} , = , - \dfrac{3}{4} , \therefore , X _C , - , X _L , = , -\dfrac{3}{4} R.$
AS, $Z^2 , = , R^2 , + , (X _C , - , X _L)^2$
$\therefore , (25)^2 , = , R^2 , + , \left(-\dfrac{3}{4} , R \right)^2$
$625 , = , \dfrac{25 , R^2}{16}.$
$R^2 , = , \dfrac{625 , \times , 16}{25} , , \Rightarrow , R , = , 20 , \Omega$