A LCR series circuit driven with $E_{\mathrm{rms}}=90 \mathrm{~V}$ at frequency $f_d=30 \mathrm{~Hz}$ has resistance $\mathrm{R}=80 \Omega$, an inductance with inductive reactance $\mathrm{X}_{\mathrm{L}}=20.0 \Omega$ and capacitance with capacitive reactance $\mathrm{X}_{\mathrm{C}}=80.0 \Omega$. The power factor of the circuit is $\_\_\_\_$ .
Select the correct option:
A
0.8
B
0.64
C
0.9
D
0.5
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Power factor is $\cos \phi=\frac{\mathrm{R}}{\mathrm{Z}}$
$$
\begin{aligned}
& \mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}=100 \Omega \\
& \cos \phi=\frac{80}{100}=0.8
\end{aligned}
$$
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