A series L.C.R circuit with R = 3 Ω, \( X_L = 10\,\Omega \) and \( X_C = 6\,\Omega \) is connected to an a.c. source. The power factor of the circuit is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.6
The power factor of a series LCR circuit is \( \cos\phi = R/Z \), where the impedance is \( Z = \sqrt{R^{2} + (X_L - X_C)^{2}} \).
\( Z = \sqrt{3^{2} + (10 - 6)^{2}}\,\Omega = \sqrt{9 + 16}\,\Omega = 5\,\Omega \)
\( \displaystyle \cos\phi = \frac{R}{Z} = \frac{3}{5} = 0.6 \)