Parallel RLC Circuits

In this section we will take a look at an RLC circuit connected in parallel.

Let's dive straight into a real example and once again take a look at the voltage across the capacitor. Note that I've included a small 0.1m ohm resistor in the circuit to more closely model a real circuit which has an impact on how the circuit operates so that you will have less surprises when measuring such a circuit in the real world! A simple circuit with R,L,C in parallel does NOT exist so let's not bother simulating it. Note that this is still NOT exactly how a real circuit would look, but it is certainly a better starting point to begin developing intuition.

Now once again before we take a look at the measurement, see if you can work out what the output voltage may look like, the one hint I'll give you is that you may be surprised by what you see!

Yep! That's what the voltage across the capacitor actually looks like! A little mind blowing right, good old nature :)

So what is going on here? Well let's once again think in terms of first principles. If we assume the circuit has been off and we apply the 5V square wave then we will send an electromagnetic wave down the circuit through the small internet resistance and then the parallel R, L and C components in parallel simultaneously. The parallel resistance will simply dissipate energy in the form of heat, meanwhile the inductor will oppose the change in current by inducing a voltage in the direction of the square wave and the capacitor will oppose the change in voltage by building up an electric field. What happens then is that we will see a voltage very close to 5V initially as only a very small voltage will drop across Rint and then with time the inductor reduces its opposition to the change in current and the capacitor voltage builds up to the point that no current flows through it but the inductor gets to the point that it is happy with the current flowing through it and effectively becomes close to a short circuit!!!! And so what happens is we have a huge current flowing through the inductor due to the tiny resistance preceding it and larger resistance in parallel until we reach the steady state voltage of around 2.5V.

To help confirm our intuition, the plot above shows the current flowing through the inductor and yes that is in units of KA!!!! I would not recommend connecting up this circuit in the real world unless you like to see fire and smoke.

The OFF cycle is also very interesting, we initially see a NEGATIVE voltage! What on earth is that magic? Surely the software that drew the waveform is faulty!!!! Once again, beautiful nature at work :)

What's happening is the inductor was happy having the large KA current flow through it and it is not happy that the square wave is turned OFF and so how does it maintain that enormous current? By inducing a voltage which forces current to flow in the same direction which means that if we consider GND to be 0V and current is flowing then we will have the current flow through the terminal of the inductor connected to ground back through the capacitor and two parallel resistances and as they incur a voltage drop we must be at a voltage lower than ground at node Vc hence the negative part.

As per the series RLC circuit there is once again no need to spend time analyzing these circuits by hand as you will NEVER need to do this in the real world but I once again encourage you to develop mental imagery of this circuits in motion as it will serve you incredibly well.

Ready for the next module? Return to the course home.