# Help with Series RLC

#### fatboy2131

Joined Oct 5, 2007
10
Hello Everyone,

I've got a question. I am taking an on-line electronics course, and we have been doing Series RLC circuits. I have a test question (attached) that I am not sure of. Basically, it is a Series RLC circuit with no values (resistor, capacitor, inductor, supply voltage, or current) other than three voltage readings. Can someone out here explain to me how I can find out this answer? I have read twice so far my lessons on this and can't figure it out. I'm sure I'm just missing something or "overthinking' it.

Thanks!

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#### techroomt

Joined May 19, 2004
198

#### ixisuprflyixi

Joined Sep 16, 2007
52
You must be overthinking it. All voltage drops in a series circuit add up to system voltage.

#### Ron H

Joined Apr 14, 2005
7,014
You must be overthinking it. All voltage drops in a series circuit add up to system voltage.
Not true. You are forgetting about phase.
Here's my take: Since the voltages are equal, and all components have the same current flowing through them, then XL=XC=R.
Since XL=XC, the circuit must be at resonance. At resonance, the voltage across (XL+XC) will be zero, because voltage across L is 180 degrees out of phase with the voltage across C. Therefore, the supply voltage is 100V.

#### fatboy2131

Joined Oct 5, 2007
10 Nice! Thanks alot!

#### bloguetronica

Joined Apr 27, 2007
1,540
Not true. You are forgetting about phase.
Here's my take: Since the voltages are equal, and all components have the same current flowing through them, then XL=XC=R.
Since XL=XC, the circuit must be at resonance. At resonance, the voltage across (XL+XC) will be zero, because voltage across L is 180 degrees out of phase with the voltage across C. Therefore, the supply voltage is 100V.
So the AC voltages at the inductor and capacitor cancel each other because they are 180º out of phase (the capacitor is 90º behind and the inductor is 90º ahead)?

#### Ron H

Joined Apr 14, 2005
7,014
So the AC voltages at the inductor and capacitor cancel each other because they are 180º out of phase (the capacitor is 90º behind and the inductor is 90º ahead)?
That's correct. Below is a Bode plot of the circuit. It's a little busy, but you can see that at 1kHz (resonance), the voltage across each element is 100V, and the phase across L and C are 180 degrees apart. You can also see that the voltage across the LC combination (V(A,C)) is zero.
Note that R=100, XC=100, and XL=100 at 1kHz. They could actually have any value, so long as all 3 are equal.

#### Ron H

Joined Apr 14, 2005
7,014
I hate how this forum converts .PNG to .JPG. It screws up the quality of the images, and also shrinks them, making them difficult to read. The other forum I lurk in doesn't convert the image format.

#### ixisuprflyixi

Joined Sep 16, 2007
52
Thank you Ron, I overlooked that. Hope I didnt confuse anyone.