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Parallel RLC Circuits: What Are They and How Do They Work?

Without them, our modern world would crumble.

Parallel RLC Circuits: What Are They and How Do They Work?
An electronic organ's resistors and capacitors. Raimond Spekking/Wikimedia Commons

Electrical circuits transport alternating or direct current through closed-loop interconnections between electrical components. Different arrangements and configurations of these components make different kinds of circuits, and RLC circuits is one of them.

What are their main characteristics and applications? What’s the role of RLC in electronics? What’s the difference between RLC series and parallel circuits? All of these questions have an answer.

Unpacking RLC

RLC stands for resistor (R), inductor (L), and capacitor (C). These are the main components of the RLC circuits, connected in a complete loop.

The resistor is made of resistive elements (like carbon) whose function is to induce more levels of electrical resistance than the natural ones that affect the circuits. It also reduces the damping and the resonant frequency in the circuit (fr).

The inductor stores energy in the magnetic fields produced by the electric current flowing through conductors, according to Faraday’s law.

The capacitor stores energy in the electric fields, through two or more conductors, most commonly separated by a dielectric medium. The measurement of that 'storability' is called capacitance.

What is a parallel RLC circuit?

In a parallel RLC circuit, the resistor, the inductor, and the capacitor are connected in parallel and share a connection to the same voltage source. This is distinct from being connected in series.

In AC RLC parallel circuits, the electrical current splits, and all the components receive the same voltage and the current is divided in each component depending on its impedance. The current doesn’t flow in parallel RLC circuits using a DC source with the same efficiency because the inductor acts as a short circuit and the capacitor acts as an open circuit.

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RLC parallel circuit

To calculate the total current, the total voltage, and the total resistance of an RLC circuit, we can use Ohm's law’s, in which the current (I) measured in amperes is equal to the voltage (V) measured in volts multiplied by the resistance (R) measured in ohms (Ω):

V=IR or, according to the units: V = A x Ω

If this formula is applied to the capacitor of the circuit, R is replaced by Xc, where Xc is the capacitive reactance. And when applied to inductors, R is replaced by Xl, where Xl is the inductive reactance

V= IXc 

V= IXl

What is impedance?

Electrical impedance is the measurement of the opposition to the current within a circuit. In spite of their similarities, impedance is not the same as resistance because the concept actually encompasses both the resistance and reactance produced in AC circuits (there is no reactance in the stable current of DC circuits).

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At resonance, both capacitive and inductive reactance will be equal to each other. The inductor and capacitor will also be conducting more current at the resonant frequency.

The equation for a parallel RLC circuit produces complex impedance’s for each parallel branch, as each element becomes the reciprocal of impedance, ( 1/Z ). The reciprocal of impedance is called admittance (Y). The inverse of the total impedance (ZRLC) is the sum of the inverse impedances of each component:

1/ ZRLC = 1/ZR + 1/ZL + 1/ZC. In other words, the total admittance of the circuit is the sum of the admittances of each component.

Otherwise, the formula to find the impedance is Z=V/I, where Z is the impedance, V is the voltage, and I is the current of the circuit.

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The inverse of the total impedance is the sum of the inverse impedances of each component. In other terms, the total admittance (the measure of how easily a circuit or device will allow a current to flow) of the circuit is the sum of the admittances of each component.

What is the use of parallel RLC circuit?

RLC circuits are often used as oscillator circuits because they produce sine waves, square waves, or triangle waves. These are oscillating electronic signals that can convert direct current into alternating current or work as a low-pass filter, high-pass filter, band-stop filter, and band-pass filter. 

As a band-pass filter, it is used for tuning, such as in television sets and analog radio receivers, which basically let you find a specific frequency range after gathering all the reachable ambient radio waves through an antenna. Band-pass filters are also used in audio equalization, audio design, and audio recording in studio. 

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Audio recording
Source: Grooveaddicted/Pixabay

As an oscillator circuit, it must have low damping values in order to work efficiently. In other words, it must have a high quality factor (Q). The parallel RLC circuit quality factor is the inverse of the series circuit quality factor.

Q = R 𝐶 𝐿 = 𝑅 𝜔0 = 𝜔0 𝑅𝐶 

Frequently asked questions about RLC Circuits

Are LCR and RLC circuits the same?

Yes, what changes is the order of the symbols. 

What is reactance?

The reactance is the opposition of a component to the stream of current because of the effect of inductance or capacitance caused by that component. 

Just like what happens with resistance, the more reactance that a circuit has, the more limited is the current it derives. But unlike resistance, the reactance changes the phase and doesn’t dissipate the electricity; instead, it stores it. 

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The reciprocal of reactance is susceptance, which measures theease at which a reactance (or a set of reactances) allows an alternating current to flow when a voltage of a given frequency is applied.

What are the differences between RLC parallel circuit and RLC series circuits?

Not only are there two different types of RLC circuits, but they also behave in effcetively opposite ways:

  • If the resistor, inductor, and capacitor are connected in parallel in parallel RLC circuits, they’re connected in series in RLC series circuits.
  • The current is the same in all the components of the circuit in RLC series circuits, but in RLC parallel circuits, the total current is equal to the vector sum of the current of each element: Is2 = IR2 + (IC – IL)2

    To calculate the current of each element, we must use the formula IR = V / R , IC = V / XC , IL = V / XL

    The same thing happens with voltage, but reversely. Voltage is different for all components in RLC series circuits and equal in RLC parallel circuits.

    To calculate the voltage in RLC series circuits, we must use VR= IR, VL = I XL, VC = I XC  

  • At resonance, RLC parallel circuits show maximum impedance, but RLC series circuits show minimum impedance. 
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