```
RLC CIRCUIT
```

The circuit which consists of resistor-capacitor and inductor is an RLC circuit it may be connected in series or in parallel. Thus it forms a harmonic oscillator it could be also called as a second order circuit as any voltage or current can be described by a second-order differential equation for the analysis of the circuit

Tuned circuit has many applications like oscillating circuits and for the radio communications it can be used to select a certain range of frequencies from the total spectrum of ambient radio waves RLC circuits are used to tune the frequencies of AM/FM radios it can be used as a band pass and band stop filter

The most important property of this circuit is its ability to resonate at a specific frequency

ɯ0 - 2πf0

f0= the resonance frequency ɯ0= angular frequency

Resonance has occurred because its energy is stored in two different ways

when the capacitor is charged it stores energy in the form of electric field and in the form of a magnetic field as the current flow through the inductor the transferring of energy from one to the other can be possible in this circuit and it could be oscillatory

**SERIES RLC CIRCUIT**

The three components in this circuit are in series with the voltage source

With the help of the given parameters, we could find the charge Q by using Kirchhoff’s voltage law

VR + VL + VC = V

**IMPEDANCE OF SERIES RLC CIRCUIT**

RLC circuit in series has inductance and capacitance XL and XC has opposite effect for the circuit phase angle and thus the total reactance is less than the individual reactance

If XL > XC the circuit is inductive

If XC > XL the circuit is capacitive

Then the total reactance is (XL - XC)

The total impedance of RLC circuit in series is θ= tan-1(Xtot/ R)

Xtot is total reactance

**VOLTAGE IN SERIES COMBINATION OF L AND** C

In RLC the capacitive and inductive voltage are 180 degrees out of phase with each other because they are in this phase they subtract from each other and thus the voltage across the L and C is combined will be less than the individual

SERIES RESONANCE

In resonance condition the magnitude of capacitive and inductive reactance is equal and thus it has a purely resistive impedance

**PARALLEL RLC CIRCUIT**

• The parallel LC resonant circuit is mostly known as the tank circuit

• Its impedance is infinity at resonance

• In the case of the bandpass filter, the critical frequency is the frequency which is above and below the resonance and the circuit response is 70% of the maximum response

The parallel RLC is the opposite of the series the applied voltage remains the same in the components and the supplied current gets divided the total current from the supply is not equal to the sum of the flow of the current in individual component but the vector sum is equal as the current flow of the resistor inductor and capacitor are not in the same phase it can’t be added arithmetically

**APPLICATIONS OF THE RESONANT RLC CIRCUIT**

• It could be used for the tuning process of an oscillator circuit, radio receiver and television sets

• Series RLC circuit does the signal processing and communication system

• Resonant series LC circuit does the voltage magnification

• Parallel and series LC circuit is used for induction heating

**DIFFERENCE BETWEEN SERIES AND PARALLEL RLC CIRCUIT**

• Resistor, capacitor, and inductor are connected in series, resistor inductor and capacitor are connected in parallel

• current is same in each element in series it is different in each element for parallel

• Different voltage for each element in series

voltage across is the same for each element in parallel

• impedence is more convenient for calculation in series Admittance is convinient for calculation in parallel

• The circuit has minimum impedance when XL = XC at resonance in series the circuit has maximum impedance when XL = XC at resonance in parallel