Explanation:
It is given that,
Resistance of the resistor, R = 2.6 ohms
Inductance, [tex]L=120\ \mu H=120\times 10^{-6}\ H[/tex]
Capacitance, [tex]C=88\ \mu F=88\times 10^{-6}\ F[/tex]
Frequency, f = 120 Hz
(a) The power factor of the series RLC circuit is given by :
[tex]P=\dfrac{R}{Z}[/tex]
Z is the impedance of the LCR circuit.
Z is given by :
[tex]Z=\sqrt{R^2+(X_L-X_C)}[/tex]
[tex]Z=\sqrt{R^2+(2\pi f L-1/2\pi f C)}[/tex]
[tex]Z=\sqrt{2.6^2+(2\pi \times 120\times 120\times 10^{-6}-\dfrac{1}{2\pi \times 120\times 88\times 10^{-6}})^2}[/tex]
Z = 15.204 ohms
The power factor is given by :
[tex]P=\dfrac{2.6}{15.204}[/tex]
P = 0.171
The power factor of the series LCR series circuit is 0.171
(b) The phase angle is given by :
[tex]cos\theta=\dfrac{R}{Z}[/tex]
[tex]\theta=cos^{-1}(\dfrac{R}{Z})[/tex]
[tex]\theta=cos^{-1}(0.171)[/tex]
[tex]\theta=80.154^{\circ}[/tex]
Hence, this is the required solution.
