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A coil of inductive reactance $31\,\Omega$ has a resistance of $8\,\Omega$. It is placed in series with a condenser of capacitive reactance $25\,\Omega$. The combination is connected to an a.c. source of 110 volt. The power factor of the circuit is :-
A
0.56
B
0.64
C
0.80
D
0.33
Detailed Solution
Power factor $= \cos\phi = \dfrac{R}{|Z|}$
Impedance of the series LCR circuit: $Z = \sqrt{R^2 + (X_L - X_C)^2}$
$Z = \sqrt{8^2 + (31 - 25)^2} = \sqrt{8^2 + 6^2}$
$Z = \sqrt{64 + 36} = 10\,\Omega$
$\cos\phi = \dfrac{8}{10}$
$\cos\phi = 0.80$
The source voltage of 110 V is not needed for the power factor.
Impedance of the series LCR circuit: $Z = \sqrt{R^2 + (X_L - X_C)^2}$
$Z = \sqrt{8^2 + (31 - 25)^2} = \sqrt{8^2 + 6^2}$
$Z = \sqrt{64 + 36} = 10\,\Omega$
$\cos\phi = \dfrac{8}{10}$
$\cos\phi = 0.80$
The source voltage of 110 V is not needed for the power factor.