# Why is a parallel RLC circuit usually driven by a current source?

Almost always when I see an example of a parallel RLC/LC circuit diagram online, the circuit is driven by a current source instead of a voltage source. On the other hand, the series RLC is always driven by a voltage source. Why is this? Why don't we drive parallel circuits with a voltage source?

• I've seen plenty of examples of parallel circuits with voltage sources. I think what you're seeing is just a coincidence. – knzhou Dec 16 '18 at 20:19
• As @knzhou is saying we have all seen plenty of parallel circuits driven by a voltage source but then there is no really interesting question one can ask. IOW it is not why they are driven that way but rather what happens when driven that way. Since we know what the voltage is on each R,L or C terminal pair there is nothing to ask unlike if they driven by a current source. In the latter case you have to work your way through the problem. – hyportnex Dec 16 '18 at 20:35
• @hyportnex That's a tempting answer, but not quite right. You could still ask "how much current comes from the voltage source as a function of frequency?" – DanielSank Dec 16 '18 at 20:41

In a parallel RLC, the voltage across each element is the same. Therefore, if you hook a parallel RLC to to a voltage source, you might think the only things remaining to calculate are the currents through each element, and it's not immediately obvious how those currents relate to the resonance properties of the circuit. On the other hand if you use a current source and calculate the voltage across the LRC you easily see the resonance properties, e.g. the voltage peaks near the resonance [a]. Similarly, for a series circuit the thing that's constant in each element is the current.

Therefore, one answer here could be that pedagogical materials use a current source with parallel circuits because doing so provides a clear route to illustrating resonance phenomena. That's not a very good answer though for two reasons. First, you could put a voltage source on a parallel RLC resonator and calculate the total current coming from that voltage source. If you do that, you'll see the resonance properties. Second, this is all kind of unsatisfying because in real life your driver circuit is either like a current source or like a voltage source. We can't just pretend the source is one way or another, can we?

Well actually, yes, we can because of the equivalence between current and voltage sources. A current source $$I_s$$ in parallel with an impedance $$Z$$ is equivalent to a voltage source $$V = I_s Z$$ in series with an impedance $$Z$$. With a parallel RLC, it's better to use the equivalent current source because it's easier to understand the effect that the source's own internal impedance has on the resonator. For example, consider the case where the source impedance $$Z$$ is just a resistor $$R$$. In the parallel representation we have the circuit shown below with an ideal current source connected to our RLC. The source's resistor simply adds in parallel with the resonator's own resistor! Therefore, computing e.g. the damping time for the combined circuit is particularly simple in this representation.

Parallel LRC connected to a current source

[a] Peak voltage is not the definition of resonance. See this other question.