The resistor (R), inductor (L), and capacitor(C) are the basic passive linear circuit elements. These components play a key role to form an electrical circuit in four different ways like the RL circuit, theLC电路和RLC电路。这些电路在模拟电子器件中是必不可少的,因为它们表现出大腿性能。必威网址下载一般来说,两者都是capacitorsand inductors are more preferred as compared with other basic components because the manufacturing of these can be done very easily. These elements are small in size for mostly high values of components. A single-pole filter can be formed by using both the RL and RC circuits. When the reactive elements like capacitor or inductor are connected in series/parallel with the load so that it will state whether the filter is high-pass or low-pass. The RL circuits are frequently used in RF amplifiers like DC power supplies, wherever the inductor (L) is used to supply DC bias current & block the RF from reaches back into the power supply.


An RL circuit is also known as an RL filter, resistor–inductor circuit otherwise RL network, and it can be defined as a circuit that can be built with passive circuit components like resistor and inductor through a current source or voltage source. Because of the existence of a resistor R in the perfect form of the circuit, this circuit will utilize energy similar to an RC/RLC circuit.

RL Circuit in Series
RL Circuit in Series

Consider the following RL circuit which includes a resistor and inductor using a voltage supply. Let us believe the flow of current within the circuit is I (amp) & through the resistor is IR & the inductor is IL correspondingly.

由于R&L等组件串联连接,因此组件和整个电路中的电流流量将与IR = IL = I相同。电阻器和电感器上的电压降是VR&VI

ApplyingKirchhoff电压法(i.e sum of voltage drop must be equal to apply voltage) to this circuit we get,

Once KVL (Kirchhoff voltage law) is applied to the above circuit, then we get



The RL circuit or resistor-inductor circuit is one kind of electric circuit that can be built with resistors & inductors which are connected to a voltage or current source. A first-order RL circuit mainly comprises one resistor & one inductor to form an RL circuit. Thepower factorof this circuit is low because of the inductive load like a 3-phase induction motor. Even the lamps, transformers, welding devices operate at low lagging power factors.

In the RL series circuit, the flow of current is lagging behind the voltage through an angle ‘ϕ’ due to the inductor effect. So here, the power factor (PF) can be given like the cosine of lagging angle ‘ϕ’

The power factor = Cos ϕ = Resistance/Impedance = R/Z

cosφ= r /√r2+XL2= R/√R2+ (ωL)2

The above equation can be divided with ‘R’

Cosφ= 1 /√1+(ωL /R)2

实际上,当我们有ωl>> r时,即小功率因数,分母中的“1”变得微不足道。

所以,Cosφ= r /ωl

Phasor Diagram

Thephasor diagram of the RL Series circuitis shown below:




The VR which is known as the voltage drop across the resistance = IR can be drawn within phase through the current (I).

在感应电抗的横跨电压下降是VL = IXL可以在电流的流程之前绘制,因为,电流的流动通过电感电路内的90度延迟电压。
The two voltages vector sum drops are VR & VL which are equivalent to the given voltage V.



VR= I.Rand VL= I.XL其中xL=2πflrl.

V = √(VR)2+(V.L)2

=√(IR)2+ (IXL)2


I = L = V/Z

z =√r.2+ XL2

Here, ‘Z’ is the whole resistance that is offered to the flow of AC through an RL Series circuit. So it is known as the impedance of the RL circuit and it is measured in ohms (Ω).


在RL串联电路中,流of current lags the voltage with 90o angle is called as phase angle

φ= TAN.-1 (XL/R)

The Impedance of Series RL Circuit

The series RL circuit’s impedance opposes the current flow and it is nothing but the combination of resistance (R) & inductive reactance (XL) effect of the entire circuit. The impedance ‘Z’ within ohms can be given like the following.

Z = (R2+ XL.2)0.5

从以下图像中的直角三角形,相位角φ= TAN.-1(XL/R).



When both the resistor as well as the inductor is connected in parallel connection through each other and supplied through a voltage source is known as RL parallel circuit. The circuit’s input and output voltages are Vin and Vout. Once the resistor & inductor are connected within parallel then the Vin is equivalent to Vout. However, the flow of current within these components is not the same.



Phasor Diagram

在一个平行的RC电路,主要的关系ong the voltage ¤ts can be illustrated through the vector (phasor) diagram.

Phasor Diagram
Phasor Diagram
  • 参考矢量'E'并表示RL并联电路内的电压。
  • As the flow of current throughout the resistor is within phase by the voltage across it, then IR is shown on the voltage vector.
  • The ‘IL’ lags the voltage through 90 degrees angle & can be arranged within a down direction for lagging the voltage vector through 90 degrees angle.
  • Here, both the vectors addition like IR & IL provides a result that signifies the sum (IT) otherwise line current
  • The angle ‘θ’ denotes the phase among the given line current & voltage.
  • 并行RL电路相位图如下所示。

In the case of a parallel circuit, the flow of current within every branch of a circuit performs independently of the currents within the remaining branches. The flow of current in every branch can be determined through the voltage across the branch & the resistance to flow of current in the form of either inductive reactance or resistance included within the branch.





The flow of current in both the components can form the legs for a right triangle & the whole current is the hypotenuse. So, the Pythagorean theorem is used to include these currents together through using the following equation:

IT= √IR2+ IL2

In these circuits, the phase angle by which the whole current lags the voltage is anywhere between 0 & 90 degrees. So, the angle size can be determined through whether there is an additional inductive current otherwise resistive current.


θ= tan-1(iL/IR)


The impedance of a parallel RL circuit can be defined as the whole resistance toward the current flow. It comprises the resistance that is offered from the resistive ‘R’ branch as well as the inductive reactance ‘XL’ can be offered through the inductive branch.

The parallel RL circuit’s impedance can be calculated like a parallel resistive circuit. But, since R & XL are vector quantities, so they should be included vectorially. Consequently, the impedance equation of a parallel RL circuit includes a single resistor & inductor, So the impedance formula for a parallel RL circuit is

Z = RXL/√R2+ XL.2



Z = E/IT

The parallel RL circuit’s impedance is low always as compared to the resistance otherwise inductive reactance of any branch. Due to this is the reason, every branch forms a separate lane for the flow of current, therefore decreasing the whole circuit resistance toward the flow of current.

When the branch has the highest amount of current so that has the most effect on the phase angle. So, this is reverse to a series RL circuit.




  • RF Amplifiers
  • Communication Systems
  • Filtering Circuits
  • Processing of Signal
  • Oscillator Circuits
  • 电流或电压的放大率
  • Variable Tunes Circuits
  • Radio Wave Transmitters
  • Resonant LC Circuit/RLC Circuit
  • These circuits are used as DC power supplies within RF amplifiers because the inductor (L) is used to supply DC bias current & block the RF to reach the power supply.

因此,这一切都是关于an overview of RL Circuit, RL series circuit, RL parallel circuit, phasor diagram, and its uses. Here is a question for you, what are the advantages of RL circuits?

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