RLC Circuit - Introduction, Series and Parallel RLC Circuits

Types of RLC Circuits

We know that Resistor (R), Inductor (L), and Capacitor (C) are the passive elements. We can connect these passive elements in a number of ways. For the time being, let us consider the basic connections. These are series connections and parallel connections. 

If an AC source is present in any electrical network/circuit, then it is known as an AC network/circuit. Since we are having two basic connections accordingly we will be having two types of RLC circuits. Now, let’s discuss the following two types of RLC circuits one by one.

• Series RLC Circuit
• Parallel RLC Circuit

Series RLC Circuit

In the series RLC circuit, we will connect the AC voltage source, Resistor (R), Inductor (L), and Capacitor (C) all in series. This circuit diagram is shown in the figure below. It is also called the RLC circuit in series. We know that the current is the same in series whereas the supply voltage (AC) gets divided among the passive elements. 

• Since, R, L, and C are connected in series, the equivalent impedance will be Z=R+j(ωL-1/ωC).
• By using ohm’s law, we will get V=IZ=I[R+j(ωL-1/ωC)]
• =>V=V_R+j(V_L-V_C)
• =>V=V_R²+(V_L-V_C)²
• If V_L=V_C, then V=V_R=IR. Here, voltage and current are in phase. Hence, the power factor in an RLC circuit is said to be a unity power factor. 
• If V_L>V_C, then the resultant value of V_L-V_C will be positive. Since current lags voltage, the power factor in the RLC circuit is said to be a lagging power factor. 
• If V_L>V_C, then the resultant value of V_L-V_C will be positive. Since current leads to voltage, the power factor in the RLC circuit is said to be the leading power factor. 

Parallel RLC Circuit

In a parallel RLC circuit, we will connect the AC current source, Resistor (R), Inductor (L), and Capacitor (C) all in parallel. This circuit diagram is shown in the figure below. It is also called an RLC circuit in parallel. We know that in parallel, voltage is the same whereas the supply current (AC) gets divided among the passive elements. 

• Since R, L and C are connected in parallel, the equivalent admittance will be Y=1/R+j(ωC-1/ωL).
• By using ohm’s law, we will get I=VY=V[1/R+j(ωC-1/ωL)]
• =>I=I_R+j(I_C-I_L)
• =>I=I_R²+(I_C-I_L)2
• If I_C=I_L, then I=I_R=V/R. Here, current and voltage are in phase. Hence, the power factor in an RLC circuit is said to be a unity power factor. 
• If I_C>I_L, then the resultant value of I_C-I_L will be positive. Since current lags voltage, the power factor in the RLC circuit is said to be a lagging power factor.  
• If I_C>I_L, then the resultant value of I_C-I_L will be positive. Since current leads to voltage, the power factor in the RLC circuit is said to be the leading power factor.  

In this article, we discussed the two RLC circuits, which are having series connections first and then parallel connections. We can find the voltage or current of each element present in the circuit by using the respective formula. In each circuit, we can know the relation between voltage and current of the following circuit.

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