RL Series Circuit
BE8251 Notes r2017 notes

RL Series Circuit And LR Series Circuit

RL Series Circuit And LR Series Circuit

RL Series Circuit And LR Series Circuit

RL Series circuit:

 In other words, an Inductor in an electrical circuit opposes the flow of current, ( i ) through it.

While this is perfectly correct, we made the assumption in the tutorial that it was an ideal inductor which had no resistance or capacitance associated with its coil windings.

However, in the real world “ALL” coils whether they are chokes, solenoids, relays or any wound component will always have a certain amount of resistance no matter how small associated with the coils turns of wire being used to make it as the copper wire will have a resistive value.

Then for real world purposes we can consider our simple coil as being an “Inductance”, L in series with a “Resistance”, R.

LR Series Circuit

LR Series Circuit consists basically of an inductor of inductance L connected in series with a resistor of resistance R.

The resistance R is the DC resistive value of the wire turns or loops that goes into making up the inductors coil

The above LR series circuit is connected across a constant voltage source, (the battery) and a switch.

Assume that the switch, S is open until it is closed at a time t = 0, and then remains permanently closed producing a “step response” type voltage input.

The current, i begins to flow through the circuit but does not rise rapidly to its maximum value of Imax as determined by the ratio of V / R(Ohms Law).

This limiting factor is due to the presence of the self induced emf within the inductor as a result of the growth of magnetic flux, (Lenz’s Law).

After a time the voltage source neutralizes the effect of the self induced emf, the current flow becomes constant and the induced current and field are reduced to zero.

We can use Kirchoffs Voltage Law, ( Kirchoffs Voltage Law, (KVL) to define the individual voltage drops that exist around the circuit and then hopefully use it to give us an expression for the flow of current.

Vt = VR + VL

VR = I*R

VL = i dL / dt

V(t) =  I*R + i dL / dt

Since the voltage drop across the resistor, VR is equal to IxR (Ohms Law), it will have the same exponential growth and shape as the current.

However, the voltage drop across the inductor, VL will have a value equal to: Ve(-Rt/L).

Then the voltage across the inductor, VL will have an initial value equal to the battery voltage at time t = 0 or when the switch is first closed and then decays exponentially to zero as represented in the above curves.

The time required for the current flowing in the LR series circuit to reach its maximum steady state value is equivalent to about 5 time constants or 5τ.

This time constant τ, is measured by τ = L/R, in seconds, were R is the value of the resistor in ohms and L is the value of the inductor in Henries.

This then forms the basis of an RL charging circuit were 5τ can also be thought of as “5 x L/R” or thetransient time of the circuit.

The transient time of any inductive circuit is determined by the relationship between the inductance and the resistance.

For example, for a fixed value resistance the larger the inductance the slower will be the transient time and therefore a longer time constant for the LR series circuit.

Likewise, for a fixed value inductance the smaller the resistance value the longer the transient time.

However, for a fixed value inductance, by increasing the resistance value the transient time and therefore the time constant of the circuit becomes shorter.

This is because as the resistance increases the circuit becomes more and more resistive as the value of the inductance becomes negligible compared to the resistance.

If the value of the resistance is increased sufficiently large compared to the inductance the transient time would effectively be reduced to almost zero.

RC Series circuit:

The fundamental passive linear circuit elements are the resistor (R), capacitor (C) and inductor (L).

These circuit elements can be combined to form an electrical circuit in four distinct ways: the RC circuit, the RL circuit, the LC circuit and the RLC circuit with the abbreviations indicating which components are used.

These circuits exhibit important types of behaviour that are fundamental to analogue electronics. In particular, they are able to act as passive filters.

This article considers the RL circuit in both series and parallel as shown in the diagrams.

In practice, however, capacitors (and RC circuits) are usually preferred to inductors since they can be more easily manufactured and are generally physically smaller, particularly for higher values of components.

Both RC and RL circuits form a single-pole filter.

Depending on whether the reactive element (C or L) is in series with the load, or parallel with the load will dictate whether the filter is low-pass or high-pass.

Frequently RL circuits are used for DC power supplies to RF amplifiers, where the inductor is used to pass DC bias current and block the RF getting back into the power supply.

RLC Series Circuit:

Difference between AC AND DC:

Current that flows continuously in one direction is called direct current .

Alternating current (A.C) is the current that flows in one direction for a brief time then reverses and flows in opposite direction for a similar time.

The source for alternating current is called AC generator or alternator.


One complete set of positive and negative values of an alternating  quantity is called cycle.


The number of cycles made by an alternating quantity per second is called frequency. The unit of frequency is Hertz(Hz)

Amplitude or Peak value

The maximum positive or negative value of an alternating quantity is called amplitude or peak value.

Average value:

This is the average of instantaneous values of an alternating quantity over one complete cycle of the wave.

Time period:

The time taken to complete one complete cycle.

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