# Series and Parallel Resonance LC Circuit Operation

The circuits which have L, C elements, those have special characteristics due to their frequency characteristics like frequency Vs current, voltage and impedance. These characteristics may have a sharp minimum or maximum at particular frequencies. The applications of these circuits mainly involve in transmitters, radio receivers and TV receivers. Consider an LC circuit in which capacitor and inductor both are connected in series across a voltage supply. The connection of this circuit has a unique property of resonating at a precise frequency termed as resonant frequency. This article discusses about what is an LC circuit, resonance operation of a simple series and parallel LC circuit.

## What is an LC Circuit?

An LC circuit is also called a tank circuit, tuned circuit or resonant circuit, is an electric circuit built with a capacitor denoted by the letter ‘C’ and an inductor denoted by the letter ‘L’ connected together. These circuits are used for producing signals at a particular frequency or accepting a signal from a more composite signal at a particular frequency. LC circuits are basic electronics components in various electronic devices, especially in radio equipment used in circuits like tuners, filters, frequency mixers and oscillators. The main function of an LC circuit is generally to oscillate with minimum damping.

### Series LC Circuit Resonance

In the series LC circuit configuration, the capacitor ‘C’ and inductor ‘L’ both are connected in series that is shown in the following circuit. The sum of the voltage across the capacitor and inductor is simply the sum of the whole voltage across the open terminals. The flow of current in the +Ve terminal of the LC circuit is equal to the current through both the inductor (L) and the capacitor (C)

** **** v = v _{L} + v_{C}**

** i = i _{L} =i_{C}**

When the ‘X_{L}’ inductive reactance magnitude increases, then the frequency also increases. In the same way while ‘X_{C}’capacitive reactance magnitude decreases, then the frequency decreases.

At one specific frequency, the two reactances X_{L} and X_{C} are the same in magnitude but reverse in sign. So this frequency is called the resonant frequency which is denoted by for the LC circuit.

Therefore, at resonance

**X _{L} = -X_{C}**

**ωL = 1/ ωC**

**ω = ω0 = 1/ √LC**

Which is termed as the resonant angular frequency of the circuit. Changing angular frequency into frequency, the following formula is used

**f0 = ω0/ 2π √LC**

In a series resonance LC circuit configuration, the two resonances X_{C} and X_{L} cancel each other out. In actual, rather than ideal components, the flow of current is opposed, generally by the resistance of the windings of the coil. Therefore, the current supplied to the circuit is a max at resonance.

An acceptance circuit is defined as when the In the Lt f f0 is the maximum and the impedance of the circuit is minimized.

For f<f0, X_{L} << (-X_{C}). Thus, the circuit is capacitive

For f<f0, X_{L}>> (-X_{C}). Thus, the circuit is inductive

### Parallel LC Circuit Resonance

In the parallel LC circuit configuration, the capacitor ‘C’ and inductor ‘L’ both are connected in parallel that is shown in the following circuit. The sum of the voltage across the capacitor and inductor is simply the sum of the whole voltage across the open terminals. The flow of current in the +Ve terminal of the LC circuit is equal to the current through both the inductor (L) and the capacitor (C)

**v = v _{L} = v_{C}**

** i = i _{L }+ i_{C}**

Let the internal resistance ‘R‘ of the coil. When two resonances X_{C} and XL, the reactive branch branch currents are the same and opposed. Therefore, they cancel out each other to give the smallest amount of current in the key line. When the total current is minimum in this state, then the total impedance is max.The resonant frequency is given by

** f0 = ω0/ 2π = 1/2π √LC**

Note that the current of any reactive branch is not minimum at resonance, but each is given individually by separating source voltage ‘V’ by reactance ‘Z’.

Hence, according to Ohm’s law **I=V/Z**

A rejector circuit can be defined as, when the line current is minimum and total impedance is max at f0 , circuit is inductive when below f0 and the circuit is capacitive when above f0

#### Applications of LC Circuit

- The applications of the resonance of the series and parallel LC circuits mainly involve in communications systems and signal processing
- The common application of an LC circuit is, tuning radio TXs and RXs. For instance, when we tune a radio to an exact station, then the circuit will set at resonance for that specific carrier frequency.
- A series resonant LC circuit is used to provide voltage magnification
- A parallel resonant LC circuit is used to provide current magnification and also used in the RF amplifier circuits as the load impedance, the amplifier’s gain is max at the resonant frequency.
- Both series and parallel resonant LC circuits are used in induction heating
- These circuits perform as electronic resonators, which are an essential component in various applications like amplifiers, oscillators, filters, tuners, mixers, graphic tablets, contactless cards and security tags X
_{L }and X_{C}

Thus, this is all about LC circuit, operation of series and parallel resonance circuits and its applications. We hope that you have got a better understanding about this concept. Furthermore, any queries regarding this concept or electrical and electronic projects, please give your valuable suggestions in the comment section below. Here is a question for you, what is the difference between series resonance and parallel resonance LC Circuits?

**Photo Credits:**

- LC Circuit wikimedia
- Series LC Circuit Resonance stack.imgur
- Parallel LC Circuit Resonance learnabout-electronics