Question

An RLC series circuit has a 2.60 Ω resistor, a 120 µH inductor, and an 88.0 µF capacitor. (a) Find the power factor at f = 120 Hz. 0.067 Correct: Your answer is correct. (b) What is the phase angle (in degrees) at 120 Hz? 3.29 Incorrect: Your answer is incorrect. °

Answer 1

Explanation:

It is given that,

Resistance of the resistor, R = 2.6 ohms

Inductance, $L=120\ \mu H=120\times 10^{-6}\ H$

Capacitance, $C=88\ \mu F=88\times 10^{-6}\ F$

Frequency, f = 120 Hz

(a) The power factor of the series RLC circuit is given by :

$P=\dfrac{R}{Z}$

Z is the impedance of the LCR circuit.

Z is given by :

$Z=\sqrt{R^2+(X_L-X_C)}$

$Z=\sqrt{R^2+(2\pi f L-1/2\pi f C)}$

$Z=\sqrt{2.6^2+(2\pi \times 120\times 120\times 10^{-6}-\dfrac{1}{2\pi \times 120\times 88\times 10^{-6}})^2}$

Z = 15.204 ohms

The power factor is given by :

$P=\dfrac{2.6}{15.204}$  

P = 0.171

The power factor of the series LCR series circuit is 0.171

(b) The phase angle is given by :

$cos\theta=\dfrac{R}{Z}$

$\theta=cos^{-1}(\dfrac{R}{Z})$

$\theta=cos^{-1}(0.171)$

$\theta=80.154^{\circ}$

Hence, this is the required solution.