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

Last updated date: 13th Jul 2024
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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.

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
$\cos \varphi =\dfrac{V_r}{V} \\ \text{where}\,\,V=\sqrt{V{{r}^{^{2}}}+{{(VL-VC)}^{2}}}$
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).