# RLC series question

Discussion in 'Electronics Homework Help' started by 2nowman, Nov 11, 2017.

1. ### 2nowman

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Nov 11, 2017
Hi, and thanks for looking.

I've been working on a practice question where i need to determine the voltage dropped across a resistor (470 ohm), an inductor (50mH) and a capacitor (900uF) arranged in series - the source is 100V AC with a frequency of 100kHz.

The voltages i've come up with are:
resistor = 1.49V
inductor = 99.9V
capacitor = 5.6uV <- this looks suspect.

I would normally check my work with the Falstad simulator applet, but in this case it doesnt agree with me, and i'm just wondering if the frequency is causing the issues as it seems insanely high to me, compared to the other component values.

Thanks again for looking, and any help is much appreciated.

2. ### kellys_eye

4,275
1,147
Jun 25, 2010
Looks like it should have read 100Hz, not 'kHz' - what results do you get at 100Hz?

3. ### 2nowman

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Nov 11, 2017
Hi kellys_eye, thanks for getting back to me on this, and using 100Hz i get:
resistor = 99.64V
inductor = 0.37V
capacitor = 6.66V
current = 212mA
which looks much more sensible to me.

resistor = 100.63V
inductor = 6.56V
capacitor = 230uV (and steadily increasing)
current = 212.4mA
The minor differences are probably due to my rounding (not sure about the cap voltage though).

The problem is that i've been given an assignment with the frequency of 100kHz, so i'm not sure what to do with this now, as the values i've been given for this problem lead onto other questions for parallel RLC circuits.

Thanks again for looking.

4. ### 2nowman

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Nov 11, 2017
The next question as mentioned is a parallel RLC circuit, but this time a variable frequency is stated...
For the first part I need to calculate the resonant frequency, but my calculator just gives me a 'maths error' ... the equation i'm using is:

Maybe its the other component values that are causing an issue (470ohm resistor, 50mH inductor and a 900uF cap), or it could just be me, either way i'm very confused now.

5. ### Ratch

1,094
334
Mar 10, 2013
What's the problem? Your calculations for 100 kHz are correct. Why assume another frequency? Your calculations for 100 Hz are sort of correct, except you have the inductor and capacitor voltages interchanged. Perhaps you should show us your calculations.

Ratch

6. ### Ratch

1,094
334
Mar 10, 2013
Where is that formula you posted coming from? What you have to do is find the frequency where the inductive reactance and capacitive reactance equal each other. Can you do it? It's not hard.

Ratch

7. ### 2nowman

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Nov 11, 2017
sorry, i pasted the image of my equation last time, hopefully it will work this time...

The first question in my original post was because i found 99.9V dropped across the inductor and only 1.49V dropped across the resistor, which seems wrong to me (please note i've only been studying AC for the last 2 days).
I couldnt get Falstad to agree with the first set of results i came up with, which is why i questioned it, but it could be me that had made a mistake somewhere.

8. ### Ratch

1,094
334
Mar 10, 2013
Well, your calculations were correct, so either you don't know how to run Falstad, or it has a bug in it. Now, how about getting the formula for resonance squared away.

Ratch

9. ### 2nowman

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Nov 11, 2017
completing the division under the root gives me:

which then becomes negative after the subtraction, obviously giving the 'maths error' when trying to calculate the root.

Bed time for me now or i will never sleep, maybe things will become more clear tomorrow.

Thanks for the help btw.

10. ### Ratch

1,094
334
Mar 10, 2013
You need to show the derivation of the resonance formula. Up to now, all you posted is a bunch of numbers..

Ratch

11. ### 2nowman

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Nov 11, 2017
The full formula i'm using is:

and i was trying to find the resonant frequency of this circuit:

I'm not really sure how to approach this circuit, so i'm making it up as i go along... on the first attempt i'd ignored the 990k resistor (which could be where i've gone wrong) - I thought i could use the above formula to calculate the resonant frequency for the parallel part of the circuit.

12. ### Ratch

1,094
334
Mar 10, 2013
Resonance occurs when the inductive reactance equals the capacitve reactance.Therefore:

Plug in the values for L and C to get a resonant frequency of 23.73 Hz. Notice that R has nothing to do with the resonant frequency for this circuit. Now, if you inserted some R in series with L or C, that would be different.

Ratch

13. ### 2nowman

7
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Nov 11, 2017
We were given this as an example to work through:
A 100uF capacitor is connected in parallel with a coil of resistance 10ohm and inductance 0.1H. If the circuit is connected to a 240V variable frequency supply, calculate:
a) the resonant frequency, b) the dynamic impedance, c) the Q factor, d) the current taken from the supply.

The answers to the questions are given and a) was found using:

are you saying this is wrong?

i really wanted to get to grips with this (which is the distinction part of an assignment), but because i only study part time and have other committments, it's almost impossible to have more than about an hour studying time. Considering i don't really understand (especially as our tutor doesnt explain things very well), and i've no idea where to go with this, i'm going to fail... i'll probably pass the course, but not getting this is a fail in my eyes.

Thanks again for the help, it is much appreciated.

Last edited: Nov 12, 2017
14. ### Ratch

1,094
334
Mar 10, 2013
Yes, it is wrong. I don't know where that formula you posted comes from. But, for an ideal coil, cap, or resistor in parallel, the equation I gave you is correct. Now, if the coil or capacitor contained some resistance, the formula would be different. You can find the resonant frequency by setting the imaginary part of the impedance to zero and solving for "f". See this link http://www.electronics-tutorials.ws/accircuits/parallel-resonance.html .

Ratch

Last edited: Nov 12, 2017