# RLC Circuit - Introduction, Series and Parallel RLC Circuits

By Mohit Uniyal|Updated : May 19th, 2022

As the name implies, the RLC circuit consists of the passive elements Resistor (R), Inductor (L), and Capacitor (C). If we study and understand the behavior of these passive components individually, then we can design the filters, oscillators &, etc., by combining these passive elements. Hence, RLC circuits play a vital role in network design/synthesis.

In this article, get an overview of RLC circuits of basic configurations and how to calculate the voltage or current of each element present in the circuit. You will also get to know the relation between voltage and current of the overall circuit. Using this information, we can conclude that the power factor in an RLC circuit is either lagging / leading or unity.

## 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=VR+j(VL-VC)
• =>V=VR2+(VL-VC)2
• If VL=VC, then V=VR=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 VL>VC, then the resultant value of VL-VC will be positive. Since current lags voltage, the power factor in the RLC circuit is said to be a lagging power factor.
• If VL>VC, then the resultant value of VL-VC 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=IR+j(IC-IL)
• =>I=IR2+(IC-IL)2
• If IC=IL, then I=IR=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 IC>IL, then the resultant value of IC-Iwill be positive. Since current lags voltage, the power factor in the RLC circuit is said to be a lagging power factor.
• If IC>IL, then the resultant value of IC-IL 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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## FAQs on RLC circuits.

• If the Resistor (R), Inductor (L), and Capacitor (C) are all connected in series with the AC voltage source, then we can say that circuit is a series RLC circuit. In this circuit, the current flow through all the network elements is the same, but only the supply voltage (AC) will get divided among the passive elements.

• In a series RLC circuit, if VL=VC, then the resultant value of VL-VC is zero. That implies, V=VR=IR. Since the voltage and current are in phase, the power factor in this circuit is said to be the unity power factor. Similarly, in a parallel RLC circuit, if IL=IC, then the resultant value of IL-IC is zero. That implies, I=IR=VR. Since the current and voltage are in phase, the power factor in this circuit is said to be the unity power factor.

•  In a series RLC circuit, if VC>VL, then the resultant value of VC-VL will be positive. Since current leads to voltage, the power factor in this circuit is said to be the leading power factor. Similarly, in parallel RLC circuit, if IC>IL, then the resultant value of IC-IL will be positive. Since current leads to voltage, the power factor in this circuit is said to be the leading power factor.

• In series RLC circuit, if VL>VC, then the resultant value of VL-VC will be positive. Since current lags voltage, the power factor in this circuit is said to be a lagging power factor. Similarly, in parallel RLC circuit, if IL>IC, then the resultant value of IL-IC will be positive. Since current lags voltage, the power factor in this circuit is said to be lagging power factor.

• If the Resistor (R), Inductor (L), and Capacitor (C) are all connected in parallel with the AC current source, then we can say that circuit is a parallel RLC circuit. In this circuit, the voltage across each network element is the same, but only the supply current (AC) will get divided among the passive elements.