It is now time to see what happens when we have resistors, capacitors and inductors in a circuit! These are known as RLC circuits or second order circuits as we now have two types of energy storage components in the circuit.
In this section we will take a look at connecting the components in series.
Let's begin by exploring the simplest configuration shown below:
Now let's simulate a real circuit with a 5v square wave voltage source with a period of 1ms connected to a resistor, inductor and capacitor with values as shown below:
What will the voltage across the capacitor look like with time? Can you guess what it will look like during the on and off periods of the square wave? Recall that inductors resist changes in current and capacitors resist changes in electric voltage. Have a quick think about how the voltage across the capacitor would change in time before we inspect the waveform below:
What we see is a rapid voltage ramp up, i.e. steep slope (gradient) which reduces with time as the voltage asymptotes towards the source voltage, 5V in this case during the ON period and the opposite effect during the off period.
So why is this the case? Initially a large current will attempt to flow as the square waveform switches to the ON state and due to this large change in current the inductor will strongly oppose it by producing a voltage in the opposite direction to prevent the change in current but as time passes the magnetic flux through the inductor approaches a steady-state value which means the inductor stops opposing the change in current and reduces its voltage opposition allowing more of the current to flow onto and off the capacitor.
When we switch to the OFF state the inductor wants to maintain the current flowing through it (which it had during the ON state) and so the capacitor initially does not lose charge quickly however with time once again the inductor see's smaller and smaller changes in flux to reduce the current flowing through it eventually having the capacitive effect dominate draining the capacitor towards 0V with time.
There is no need to spend time analyzing these circuits by hand as you will NEVER need to do this in the real world, understanding these circuits intuitively however is of critical importance. I encourage you to spend time thinking about the above to the point you can visually see what is happening in your head, I promise it will serve you very well as at the end of the day ALL passive circuits resolve to an RLC connected circuit.