What is RL Circuit : Working & Its Uses

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, the LC circuit & the RLC circuit. These circuits are essential in analog electronics as they exhibit thigh performance. Generally, both the capacitors and 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.

What is RL Circuit?

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

This is not like the perfect form of an LC circuit, which will use no energy because of the nonexistence of a resistor. Even though, this is simply in the perfect form of the circuit. Practically, even an inductor-capacitor circuit will use some energy due to the not existence of resistor & connecting wires.
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.

Since both the components like R & L are connected in series, then the flow of current within both the components & the entire circuit will be the same like IR = IL = I. The voltage drop across the resistor and inductor are VR & VI

Applying Kirchhoff voltage law (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

V = VR +VL

Power Factor

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. The power factor of 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

Cos ϕ = R/√R2+XL2 = R/√R2+ (ω L)2

The above equation can be divided with ‘R’

Cos ϕ = 1/√1+ (ω L/R)2

In fact, when we have ω L>>R, that is a small power factor, the ‘1’ in the denominator becomes insignificant.

So, Cos ϕ = R/ ω L

Phasor Diagram

The phasor diagram of the RL Series circuit is shown below:

Phasor Diagram of Series Circuit
Phasor Diagram of Series Circuit

The following steps give instructions step by step to draw the phasor diagram.

Here, current (I) can be taken as a reference.

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

Across the inductive reactance, the voltage drop is VL = IXL can be drawn ahead of the flow of current because, the flow of current lags voltage through 90 degrees of angle within the Inductive circuit.
The two voltages vector sum drops are VR & VL which are equivalent to the given voltage V.


In the above triangle like OAB

VR = IR and VL = IXL where XL = 2πfLRL

V = √(VR)2+ (VL)2

= √(IR)2+ (IXL)2

= I è2+ (XL)2

I = L = V/Z

Z = √R2 + 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).

Phase Angle

In RL series circuit, the flow 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 + XL2)0.5

From the right angle triangle in the following images, phase angle ϕ = tan-1 (XL/R).


RL Parallel Circuit

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.

RL Parallel Circuit
RL Parallel Circuit

This kind of circuit cannot be used as a filter for voltages because both the input & output voltages in this circuit are equal. So due to this reason, this circuit is not frequently used as evaluates to series RL circuit.

Phasor Diagram

In a parallel RC circuit, the main relationship among the voltage &currents can be illustrated through the vector (phasor) diagram.

Phasor Diagram
Phasor Diagram
  • The reference vector ‘E’ & signifies the voltage within the RL parallel circuit.
  • 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.
  • The Parallel RL circuit phasor diagram is shown below.

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 current in individual branch can be determined through ohms law

IR = E/R


The flow of current within the resistive branch includes a similar phase to the given voltage; however, the current in an inductive branch lags the given voltage with 90 degrees of angle. Consequently, the whole line current includes IR and IL with 90 degrees out of stage through each other.

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.

If there is an additional inductive current, then the phase angle ‘θ’ will be nearer to 90 degrees. It will be closer to zero degrees if there is an additional resistive current. So, from the above circuit vector diagram we can observe that the phase angle value can be measured from the following equation:

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 + XL2

In the denominator of the above equation is the vector sum of the resistance & inductance resistance. So if there is above one branch of resistive & the inductive, they must equivalent for the whole resistance otherwise reactance of these parallel branches.

Once the whole current & the applied voltage are well-known, then impedance can be more simply measured by using Ohm’s law like the following.

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.

In a parallel RL circuit, if inductance is higher than resistance, then resistive branch current is superior as compared to the inductive branch current. Consequently, the phase angle among the given voltage & the whole current can be nearer to 0 degrees because it is more responsive within nature.

RL Circuit Uses

The basic components like Resistors, Capacitors, and Inductors are combined to form different circuits such as RC, RL & RLC circuits. The applications of RL circuit, RC & RLC include the following.

  • RF Amplifiers
  • Communication Systems
  • Filtering Circuits
  • Processing of Signal
  • Oscillator Circuits
  • Magnification of Current or Voltage
  • 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.

Thus, this is all about 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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