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# Impedance of parallel inductors in series with parallel capacitors

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## Impedance of parallel inductors in series with parallel capacitors

11. Two 1mH inductors are connected in parallel and in series with two 45uF capacitors connected in parallel. What is the total impedance of the circuit?

Originally Posted by slts1991
11. 0.41 miliohms

How did you come up with 0.41 milliohms? I don't see how to solve this without frequency to calculate reactance, assuming 60hz this is what i got

1mH = 2x 377 ohms in parallel= 188.50 ohms
45uF = 2x 58.9 ohms in parallel = 29.45 ohms
series 188.50 + 29.45 = 217.95 ohms
help?

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Originally Posted by Inglefles897
11. Two 1mH inductors are connected in parallel and in series with two 45uF capacitors connected in parallel. What is the total impedance of the circuit?

How did you come up with 0.41 milliohms? I don't see how to solve this without frequency to calculate reactance, assuming 60hz this is what i got

1mH = 2x 377 ohms in parallel= 188.50 ohms
45uF = 2x 58.9 ohms in parallel = 29.45 ohms
series 188.50 + 29.45 = 217.95 ohms
help?
It is 188.50 - 29.45 because they are 180 degrees apart in a 60 HZ system and when connected in series they subtract from each other. When they are in series the formula is Z = XL - XC. In parallel the formula is more complicated and is similar to R1xR2/(R1+R2). In this case it is (XL*-XC)/(XL-XC). This means that as XL-XC approach zero (resonance frequency) that the impedance of the parallel tank circuit will approach infinity at that resonant frequency, but since the reactor and capacitor have watt losses you will never get infinity and real world examples of a wave trap have been 2000 to 10000 ohms at resonant frequency. A wave trap blocks the resonant frequency from getting onto the operating bus and passes the 60 HZ, so a wave trap has to be rated to carry normal line loads. Your series resonant circuits are similar and we call those line tuners in the power line carrier world. As XL-XC approach resonant frequency the two cancel themselves out and it allows your resonant frequency to pass and it blocks your carrier frequency.

Resonant Frequency equals 1/(2 PI (LC)^.5). I know that this formula is not needed for the above mentioned problem, but it helps you understand why a problem like this may be important and helps you figure out what size capacitor and reactor is needed for a wave trap and line tuner.

So, the answer to this problem is actually 159.05.

My old Navy instructors told me that the Smithsonian had a tank circuit ran for decades and only seemed to lose power when they took measurements, but I but that was just an electronic legend, lol.

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Originally Posted by Inglefles897
11. Two 1mH inductors are connected in parallel and in series with two 45uF capacitors connected in parallel. What is the total impedance of the circuit?

How did you come up with 0.41 milliohms? I don't see how to solve this without frequency to calculate reactance, assuming 60hz this is what i got

1mH = 2x 377 ohms in parallel= 188.50 ohms
45uF = 2x 58.9 ohms in parallel = 29.45 ohms
series 188.50 + 29.45 = 217.95 ohms
help?
I came up with a completely different answer, but I see some issues in your work.

Xl = 2pifL = 2*pi*f*(.001H) = 0.377 ohms
Xc = 1/(2pifC) = 1/[2*pi*f*(.000045F)] = 58.9ohm

Inductors function like normal resistors, so parallel Xl of the same magnitude are halved ie. Xl total = 0.1885 ohm

Caps in parallel are additive, so Xc total = 117.8 ohm.

Since they act along the same axis in opposite directions, you can just subtract them now (I think) or go through whatever steps you need to resolve R and X.

I come up with about 117.6 ohm. <-90degree

Last edited by young_dad; November 26, 2019 at 08:32 AM.

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Originally Posted by tonybeavers
It is 188.50 - 29.45 because they are 180 degrees apart in a 60 HZ system and when connected in series they subtract from each other. When they are in series the formula is Z = XL - XC. In parallel the formula is more complicated and is similar to R1xR2/(R1+R2). In this case it is (XL*-XC)/(XL-XC). This means that as XL-XC approach zero (resonance frequency) that the impedance of the parallel tank circuit will approach infinity at that resonant frequency, but since the reactor and capacitor have watt losses you will never get infinity and real world examples of a wave trap have been 2000 to 10000 ohms at resonant frequency. A wave trap blocks the resonant frequency from getting onto the operating bus and passes the 60 HZ, so a wave trap has to be rated to carry normal line loads. Your series resonant circuits are similar and we call those line tuners in the power line carrier world. As XL-XC approach resonant frequency the two cancel themselves out and it allows your resonant frequency to pass and it blocks your carrier frequency.

Resonant Frequency equals 1/(2 PI (LC)^.5). I know that this formula is not needed for the above mentioned problem, but it helps you understand why a problem like this may be important and helps you figure out what size capacitor and reactor is needed for a wave trap and line tuner.

So, the answer to this problem is actually 159.05.

My old Navy instructors told me that the Smithsonian had a tank circuit ran for decades and only seemed to lose power when they took measurements, but I but that was just an electronic legend, lol.
How is everyone getting 377 ohms for XL?

2 x 3.14 x 60 x .001H = 0.377 ohms, not 377 ohms???

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Originally Posted by mmacdonell
How is everyone getting 377 ohms for XL?

2 x 3.14 x 60 x .001H = 0.377 ohms, not 377 ohms???
Not everyone! 0.377 is correct.

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