Understanding RLC Circuits: How Do I Calculate Currents for Each Component?

[Chemmjr18]

I'm having trouble understanding RLC circuits. If I have a resistor, capacitor, and inductor connected in series and I'm GIVEN the current through the resistor, How do I find the currents through each component? Is it the current that was given for the resistor (since they're in series), or do I have to calculate it using the information given? Also, what does it mean when the current leads? What about when the voltage leads? Thanks!

 

[rumborak]

Since you know the current, you know the voltage across the resistor. Now you can just treat the circuit like an LC circuit with a voltage source.

 

[Chemmjr18]

Since you know the current, you know the voltage across the resistor. Now you can just treat the circuit like an LC circuit with a voltage source.

So the currents through the capacitor and inductor are not the same as the current through the resistor (they are in series)? If this is the case, I just find the voltage across the resistor and use that voltage to find the current through the capacitor and inductor?

 

[cnh1995]

So the currents through the capacitor and inductor are not the same as the current through the resistor (they are in series)

They are. In a series circuit, current through all the components is the same.

 

[Chemmjr18]

They are. In a series circuit, current through all the components is the same.

Thanks! Also, when I'm calculating the voltages, do I need to consider the phase angle? Or do I include the phase angle into the current equation? I know that the phase angle is how much out of phase the current is with the voltage. So would I just add the phase angle to the ωt terms?

 

[cnh1995]

Thanks! Also, when I'm calculating the voltages, do I need to consider the phase angle? Or do I include the phase angle into the current equation? I know that the phase angle is how much out of phase the current is with the voltage. So would I just add the phase angle to the ωt terms?

These questions seem quite vague to me. Please post a circuit diagram. It would be better to work on an actual ac circuit problem.

 

[sophiecentaur]

Thanks! Also, when I'm calculating the voltages, do I need to consider the phase angle? Or do I include the phase angle into the current equation? I know that the phase angle is how much out of phase the current is with the voltage. So would I just add the phase angle to the ωt terms?

Have you actually done a course on EE or is the OP question out of the blue? The reason I ask is that, if you had started with the basics, it would be obvious how to tackle such problems; the basic rules for these calculations are very clear. There is very little point in diving into the middle of a topic like this; it's going to produce more and more confusion as you go on. Do you have a textbook or some notes about this?

 

[NascentOxygen]

Thanks! Also, when I'm calculating the voltages, do I need to consider the phase angle? Or do I include the phase angle into the current equation? I know that the phase angle is how much out of phase the current is with the voltage. So would I just add the phase angle to the ωt terms?

You have a series circuit, and know its current as a function of time. Current in each element is identical.

To find the voltage across the resistor you use Ohms Law, viz., $v(t) = R \cdot i(t)$

To find the voltage across the inductor you use the differential equation relating inductor voltage to its current, these both are functions of time and their relation is: $v(t)=L\cdot\frac{d\ i(t)}{dt}$

Capacitor voltage can be determined likewise.

The equations take care of phase, it needs no special treatment.

 

[Chemmjr18]

Have you actually done a course on EE or is the OP question out of the blue? The reason I ask is that, if you had started with the basics, it would be obvious how to tackle such problems; the basic rules for these calculations are very clear. There is very little point in diving into the middle of a topic like this; it's going to produce more and more confusion as you go on. Do you have a textbook or some notes about this?

The problem is that in the notes, the book, and class, the way these problems are being solved is very systematic. You're either given the voltage or current output of the source, then you find the impedance, then the peak current (or voltage), then the phase angle, and finally the current through each circuit component (or voltage). So, because these problems are solved in such fashion, it's easy to get thrown out of order when you're not starting at the beginning. That's like throwing you into a bakery, pointing to a bowl filled with some ingredients and saying "finish making this cake". It wouldn't be impossible--but it wouldn't be obvious either. And to answer your questions, no, I have not taken an EE class and no, this question is not out of the blue. I'm taking a physics 2 course. During the summer. So because it's not an EE class, and there were other topics the instructor felt were more important than this, and it's a summer class, my understanding of the basics isn't as good as it should be. This material was covered in less than 2 hours. We didn't cover RL circuits or LC. I'm assuming because the instructor saw that if you could solve an RLC circuit you could solve them all. Also, I can't necessarily rely on the book for help because, again, it--like most books--is very systematic. So because some of the material was skipped in class, it's difficult to just jump to the section on RLC circuits. I'd like to be able to go through each chapter, work the problems, and get a better understanding, but time is a real constraint because, again, it's a summer class.

 

[cnh1995]

Ok.
But still, your questions in #5 are vague. It would be better if you asked some particular questions regarding a particular ac circuit.

 

[sophiecentaur]

So, because these problems are solved in such fashion, it's easy to get thrown out of order when you're not starting at the beginning.

I sympathise but you are dealing with a complicated problem to solve. It can be baffling when a teacher says 'solve this in this way' and ' solve that in a different way'. You can't tell why they made that particular choice but you need to be dogged in your approach. You can rely on set questions to have an actual answer and that's a big help. It may not be the most efficient way (you will learn to improve) but you decide on the data you are given and what it can tell you further about the circuit. Those intermediate answers will provide an input to another equation which may then yield the required answer. After doing a number of these questions, you start to see how you could have got there quicker. It's the same process as with resistive networks but you are dealing with complex numbers (or the trig equivalents).
There is no shortage of such material available on the web and you have to get stuck in and start answering simple questions at first and work upwards. If your course is not up to standard, you are very lucky these days because there is vastly more material available than there ever was with access to just one teacher and one textbook.

 

[Chemmjr18]

Ok.
But still, your questions in #5 are vague. It would be better if you asked some particular questions regarding a particular ac circuit.

Here's a problem I did https://www.physicsforums.com/threads/rlc-circuits.920902/

 

[jim hardy]

Your thread linked in post 12 doesn't address phase angles.

Homework Equations

χL=ω*L
χC=1/(ωC)
Z=√(R2+(χL-χC)2)
φ=tan-1((χL-χC)/R)
Vi=Ii*Z

Have you learned complex arithmetic, phasor notation and operator j ? Rectangular to polar co-ordinate conversion?

X_L = jωL
X_C = 1/jωC

operator j shifts phase 90 degrees . From there it's all solvable with high school trigonometry.