This post answers the question “What is a series RL circuit?”. It shows how to make an analysis of series RL circuit with the step input signal.

The circuit and the input voltage signal are depicted below. Let’s find voltage and current wave-forms of the inductor and it’s time constant.

What is a series RL circuit
The series connection of resistor and inductor driven by voltage source
The input step function of the voltage source

Let’s consider the voltage source signal as VS(t)=0, t<0V, t0.

As in the example with the series RC circuit, we must apply KVL  iLR+LdILdt=vS. The total solution of this differential equation is the sum of homogenous and particular solution.

In order to find homogenous solution we must resolve the equation iLR+LdiLdt=0. Let’s assume that homogenous solution is in the form iL=Aest. So RAest+sLest=0, then s=RL and the homogenous solution is iL=AeRLt.

In order to find particular solution, we must resolve the equation vS=iLpR+LdiLpdt. Particular solution of this equation can be iLp=const. In this case const=VR.

So total solution is iL=VR+AeRLt. Knowing that for t=0iL=0 then A=VR. Then iL=VR(1eRL).

Here we can obtain vL=LdiLdt=VeRLt.

The current and voltage waveforms for inductor are depicted below.

What is a series RL circuit
Inductor current waveform
Inductor voltage waveform

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