Question

What is the power factor of a $RLC$ circuit?

Answer 1

Hint: In an A.C circuit the power factor Is the cosine of the angle between current and voltage. IN a RLC circuit there are resistors , inductors and capacitors in an electrical Circuit where R stands for resistor ,L for inductor and C for capacitor,R,L and C can be connected in series or in parallel or in any combination.

Complete answer:
Due to the difference in properties of inductor and capacitor of how they react with varying time the RLC circuit forms a harmonic oscillator of current. For some part of time the inductor stores energy and provides it to the capacitor and when the inductor runs out of energy the capacitor provides energy stored during the time the inductor was providing energy.

Resistor provides a damping effect to the circuit such that if there is not a source connected to the circuit the current eventually becomes zero.For a series RLC circuit given below

Given below is the voltage $V_r$ (voltage across resistor ) which is in phase with current,VL(voltage across inductor) which is 90 degree ahead of current in the circuit and Vc(voltage across capacitor) which is 90 degree behind of current in the circuit so as we power factor is the cosine of angle between current and voltage here we can see
$$\begin{gathered} \cos \phi ={\displaystyle \frac{V_r}{V}} \\ \text{where}V=\sqrt{V{r}^{{}^2}+{(VL-VC)}^2} \end{gathered}$$

Note: Power factor is also defined as the ratio of power used in the circuit to power delivered to the circuit,actual power used in the circuit will be the real power which is used by the resistance ,the power used by capacitor and inductor is called apparent power. Resistance $R$ has resistance R , inductor $L$ has reactance $X_L$ (Inductive reactance) and capacitor $C$ has reactance $X_C$ (capacitive reactance).