Diagram Fasor Rlc

A series RLC circuit consists of resistance, inductance, and capacitance in series. Whenever we apply a sinusoidal voltage across the series RLC circuit every voltage and current in the circuit will be also sinusoidal in its steady-state condition. The only difference is in its amplitude and phase angle. It is obvious that there will be no change in the frequency of the signals. In other words, the voltages across the resistance inductance and capacitance will have the same frequency as that of the source.

Response of Series RLC Circuit

Diagram Fasor Arus dan Tegangan Rangkaian Seri R-L-C. Fasor berasal dari kata ”phase” dan ”vector” dalam bahasa inggris yang artinya adalah ”vektor fase”. Fasor digunakan untuk menyatakan besaran- besaran dalam arus bolak- balik, misalnya tegangan dan arus. Diagram fasor untuk rangkaian RLC paralel dihasilkan dengan menggabungkan bersama-sama tiga fasor individu untuk setiap komponen dan menambahkan arus secara vektor. Karena tegangan melintasi rangkaian adalah umum untuk ketiga elemen rangkaian, kita dapat menggunakan ini sebagai vektor referensi dengan tiga vektor arus digambar relatif terhadap. This entry was posted in Aplikatif and tagged Cara Menghitung Rangkaian RLC, Contoh Rangkaian RLC, Contoh Soal Rangkaian RLC Seri Paralel, Daya Efektif Rangkaian RLC, Diagram Fasor Rangkaian RLC, Frekuensi Resonansi Rangkaian RLC, Fungsi Rangkaian RLC, Grafik Fasor Rangkaian RLC, Hubungan Fasa Rangkaian RLC, Latar Belakang Rangkaian RLC.

We have shown one simple basic series RLC circuit here in the figure.
The source voltage is sinusoidal and we can represent it as

The impedance of the series RLC circuit is

Therefore the current flowing through the circuit is

Now the expression of the impedance of that RLC circuit can be rewritten as

The polar form of this impedance is

Condition of Inductive Circuit

The above-mentioned series RLC circuit shows inductive nature when the inductive reactance is much much more than the capacitive reactance of the circuit.

Condition of Capacitive Circuit

The circuit shows its capacitive nature when the capacitive reactance is much much more than the inductive reactance.

The phase difference between the voltage and current is given by

Whenever the inductive reactance is much higher than the capacitive reactance this angle becomes positive. Therefore we can conclude that the current lags the voltage with this angle.

On the other hand, when the inductive reactance is much less than the capacitive reactance this angle becomes negative. In that case, the current leads the voltage with this angle.

Ultimately we can summarise that in the inductive circuit the current lags the source voltage and in the capacitive circuit the current leads the source voltage.

Phasor Diagram of Series RLC Circuit

Phasor Diagram of Inductive Series RLC Circuit

We normally take the direction of the circuit current as the reference axis of the diagram. The voltage drop across the resistance will have the same phase as that circuit current. The voltage drop across the inductive reactance will be perpendicularly upward on the current axis. This is because the voltage drop across a pure inductance has exactly 90° phase advancement in respect of the current. In other words, the current lags the voltage at exactly 90°. The voltage drop across the capacitive reactance will be perpendicularly downward on the current axis.

Phasor Diagram of Capacitive Series RLC Circuit

In contrast, across the pure capacitive element, the voltage lags the current by exactly 90°. Alternatively, we can say the current leads the voltage by exactly 90°. The resultant voltage across the entire reactive part of the circuit is the difference between inductive and capacitive voltage drops. The vector sum of the resistive voltage drop and reactive voltage drop is the source voltage of the circuit.

If the inductive voltage drop is more than the capacitive voltage drop, the resultant reactive voltage will be perpendicularly upward.

On the other hand, if the capacitive voltage drop is more than the inductor voltage drop, the resultant reactive voltage will be perpendicularly downward.

When a pure resistance of R ohms, a pure inductance of L Henry and a pure capacitance of C farads are connected together in series combination with each other then RLC Series Circuit is formed. As all the three elements are connected in series so, the current flowing through each element of the circuit will be the same as the total current I flowing in the circuit.

Contents:

The RLC Circuit is shown below:

In the RLC Series circuit

X_L= 2πfL and X_C = 1/2πfC

When the AC voltage is applied through the RLC Series circuit the resulting current I flows through the circuit, and thus the voltage across each element will be:

V_R = IR that is the voltage across the resistance R and is in phase with the current I.
V_L = IX_L that is the voltage across the inductance L and it leads the current I by an angle of 90 degrees.
V_C = IX_C that is the voltage across capacitor C and it lags the current I by an angle of 90 degrees.

Phasor Diagram of RLC Series Circuit

The phasor diagram of the RLC series circuit when the circuit is acting as an inductive circuit that means (V_L>V_C) is shown below and if (V_L< V_C) the circuit will behave as a capacitive circuit.

Steps to draw the Phasor Diagram of the RLC Series Circuit

Diagram Fasor Aruus Rangkaian Rlc Paralel

Take current I as the reference as shown in the figure above
The voltage across the inductor L that is V_L is drawn leads the current I by a 90-degree angle.
The voltage across the capacitor c that is V_c is drawn lagging the current I by a 90-degree angle because in capacitive load the current leads the voltage by an angle of 90 degrees.
The two vector V_L and V_C are opposite to each other.

Where,

It is the total opposition offered to the flow of current by an RLC Circuit and is known as Impedance of the circuit.
Phase Angle

From the phasor diagram, the value of phase angle will be

Power in RLC Series Circuit

The product of voltage and current is defined as power.
Where cosϕ is the power factor of the circuit and is expressed as:

The three cases of RLC Series Circuit

When X_L > X_C, the phase angle ϕ is positive. The circuit behaves as RL series circuit in which the current lags behind the applied voltage and the power factor is lagging.
When X_L < X_C, the phase angle ϕ is negative, and the circuit acts as a series RC circuit in which the current leads the voltage by 90 degrees.
When X_L = X_C, the phase angle ϕ is zero, as a result, the circuit behaves like a purely resistive circuit. In this type of circuit, the current and voltage are in phase with each other. The value of the power factor is unity.

Impedance Triangle of RLC Series Circuit

When the quantities of the phasor diagram are divided by the common factor I then the right angle triangle is obtained known as impedance triangle. The impedance triangle of the RL series circuit, when (X_L > X_C) is shown below:

If the inductive reactance is greater than the capacitive reactance than the circuit reactance is inductive giving a lagging phase angle.

Impedance triangle is shown below when the circuit acts as an RC series circuit (X_L< X_C)

When the capacitive reactance is greater than the inductive reactance the overall circuit reactance acts as capacitive and the phase angle will be leading.

Soal Diagram Fasor Rlc

Applications of RLC Series Circuit

The following are the application of the RLC circuit:

Gambar Diagram Fasor Rangkaian Rlc

It acts as a variable tuned circuit
It acts as a low pass, high pass, bandpass, bandstop filters depending upon the type of frequency.
The circuit also works as an oscillator
Voltage multiplier and pulse discharge circuit