# school circuit problem

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#### dnolan747

##### Member
i am having a problem with a question in my resonant circuit course... i have a circuit with a resistor, capacitor, and an inductor all in series with an AC source.... the voltage across the resistor is 100v,, the voltage across the cap. is 100v,, and the voltage across the inductor is 100v,,, and i am being asked what is the source voltage... can anyone help me with this

thanks Dean

#### Roff

##### Well-Known Member
i am having a problem with a question in my resonant circuit course... i have a circuit with a resistor, capacitor, and an inductor all in series with an AC source.... the voltage across the resistor is 100v,, the voltage across the cap. is 100v,, and the voltage across the inductor is 100v,,, and i am being asked what is the source voltage... can anyone help me with this

thanks Dean
You hopefully recognize that the current through all 3 components is the same. What are the phase relationships between voltage and current in a resistor? How about an inductor? A capacitor? If you answer those questions, and use your noggin, you can figure out the answer.

#### dnolan747

##### Member
well rof I know the in a resistor the phase relationship is equal between I and V... In a cap it is current 90deg leading and in an inductor the current is 90deg lagging if i am not mistaken... and if i am right on this i am still missing something,, for some reason i cannot picture it, i will probably feel real stupid when i finally figure it out

Thanks Dean

#### Roff

##### Well-Known Member
well rof I know the in a resistor the phase relationship is equal between I and V... In a cap it is current 90deg leading and in an inductor the current is 90deg lagging if i am not mistaken... and if i am right on this i am still missing something,, for some reason i cannot picture it, i will probably feel real stupid when i finally figure it out

Thanks Dean
You're on the right track. Instead of saying the current is leading or lagging, recognize that the current is the same phase through all 3 components. Does that make sense to you? Once you come to grips with this, what does this imply about the relative phases of the voltages across each component?

##### New Member
Find the total impedance of the circuit. The current through the 3 components is given by I = V(across resistor) / R

Now the source voltage is V (source) = I*Z

where Z is the impedance.

#### Roff

##### Well-Known Member
Find the total impedance of the circuit. The current through the 3 components is given by I = V(across resistor) / R

Now the source voltage is V (source) = I*Z

where Z is the impedance.
He has been given no values for any of the components, and the frequency of the source is not specified. How is he going to calculate Z?
He doesn't need to know Z. I already told him everything he needs to know.

#### dnolan747

##### Member
well roff I think I have it, I HOPE, there is 100v across the inductor, 100v across the capicitor, and 100v across the resistor... so i think there would be 200v across the inductor and the capicitor if measured across both and also 200v if measured across the capicitor and the resistor.. so that means if i measure across all 3 components i would get 300v and that would be my source voltage also so my answer would be source voltage=300v.... if i am not right without giving me the answer could you explain this to me cause if i am not right then i am more lost than i thought

thanks Dean

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#### Roff

##### Well-Known Member
well roff I think I have it, I HOPE, there is 100v through the inductor, 100v through the capicitor, and 100v through the resistor... so i think there would be 200v through the inductor and the capicitor if measured across both and also 200v if measured across the capicitor and the resistor.. so that means if i measure across all 3 components i would get 300v and that would be my source voltage also so my answer would be source voltage=300v.... if i am not right without giving me the answer could you explain this to me cause if i am not right then i am more lost than i thought

thanks Dean
That's not right. The only way you could get 300V, with 100V across the resistor, is if all three components were resistors. This is all about phase. I'm sure that's the lesson you are supposed to be learning here. Have you studied vectors?
The voltage across an inductor leads the current by 90 degrees. The voltage across a capacitor lags the current by 90 degrees. The current through your inductor is the same current, and therefore has the same phase, as the current through your capacitor. This should give you a big clue about the voltage across the L-C series combination.

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#### dnolan747

##### Member
the part on vectors is really short and not very informative but if i am understanding you right if the current is in phase then the voltage across the L-C combination is also 100v, right? as it was across them seperately. and by the clue you gave me as "they would all have to be resistors" then the source voltage would be the same as the resistor 100v and if this is true then this was my first answer but i doughted myself.

#### dnolan747

##### Member
this is killing me i want to understand but for some reason it is not clicking

#### Roff

##### Well-Known Member
this is killing me i want to understand but for some reason it is not clicking
Is it clear to you that when you measure the voltage across a component, the meter tells you nothing about phase (unless you are using a vector voltmeter or some other sophisticated instrument)?
Is it clear that phase is important here?
Have you studied vector arithmetic?
Answer these three questions (all three) and I will give you a bigger hint.

#### dnolan747

##### Member
yes i know the meter will tell me nothing about phase...
yes i know that phase is important but i think this is where my problem is...
and i have studied radian measurement and also speed, velocity, vector, and phasor, and as a matter of fact i have the book in front of me but the part on vecto is very short...

#### Roff

##### Well-Known Member
What are you studying? Before I studied circuit analysis, I seem to recall having a prerequisite class in complex math.
Before I give you the big clue, let's see if this rings a bell.

First, understand that I'm not trying to belittle you here. I'm just trying to see whether you can understand the answer if I give it to you.

Suppose I tell you I have an R-L (resistor-inductor) series circuit, and the voltage across the resistor is 100V, and the voltage across the inductor is 50V. I even give you a vector diagram (attached) as a clue. Can you tell me the voltage across the series R-L circuit? If not, then I don't think you have the math background to solve this problem, or perhaps to even understand the explanation.

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#### dnolan747

##### Member
i am taking an electronics technician course at Penn Foster Career school and it is online and at home in my own time, i have no one to explain to me if i have a problem but to call the school and i work in the daytime and it is hard to get with them because of my schedule so you could say i am doing this on my own i am holding a B average but now i have hit a brick wall with this resonant citcuit coarse... I know you are not belittling me and i am enjoying this just missed something i guess and i thank you very much for taking the time to help me so far and i am sorry if i am being aggrivating with my ignorance

#### dnolan747

##### Member
is there a formula for that R-L circuit??? i am having a problem with putting certain formulas with certain circuits i am just overwhelmed with formulas have so many to remember i am having to keep a list but dont know this one and i guess what might be throwing me off is that there is no other values just voltage

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#### dnolan747

##### Member
What are you studying? Before I studied circuit analysis, I seem to recall having a prerequisite class in complex math.
Before I give you the big clue, let's see if this rings a bell.

First, understand that I'm not trying to belittle you here. I'm just trying to see whether you can understand the answer if I give it to you.

Suppose I tell you I have an R-L (resistor-inductor) series circuit, and the voltage across the resistor is 100V, and the voltage across the inductor is 50V. I even give you a vector diagram (attached) as a clue. Can you tell me the voltage across the series R-L circuit? If not, then I don't think you have the math background to solve this problem, or perhaps to even understand the explanation.

I used vector addition for your problem and came up with 110v. is this correct

#### Roff

##### Well-Known Member
I used vector addition for your problem and came up with 110v. is this correct
The answer is 111.8V. The vector amplitude is the square root of the sum of the squares of the two voltages. I'm curious how you got 110V.
I admire your determination to further your education, and I'm going to post a vector diagram of your circuit, with an explanation. Hopefully, you will understand it.

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#### dnolan747

##### Member
The answer is 111.8V. The vector amplitude is the square root of the sum of the squares of the two voltages. I'm curious how you got 110V.
I admire your determination to further your education, and I'm going to post a vector diagram of your circuit, with an explanation. Hopefully, you will understand it.
well in my study material i used the graphical method instead of the math method so i took 50v and drew a 5 inch vertical line and represented one inch as 10v so 5 inches =50v.. then i drew a 10inch horizontal line for 100v.. and i drew this as a 90 degree angle then closed off the rectangle with equal oppisite sides and then drew a line from corner to corner diagnolly and it measured a little over 11 inches so i knew it was just over 110v

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#### Roff

##### Well-Known Member
141.4 doesn't take into account the presence of the capacitor in the circuit.
Look at the waveforms below. You can see that the voltage across the capacitor V(c) is 180 deg out of phase with the voltage across the inductor V(L,C), so they cancel. Note that the voltage at V(L) is zero (LTspice won't let me make the "L" a capital letter), because of the cancellation. Since the voltage across the resistor V(R,L) is 100V, the source voltage is also 100V, which is your answer.
I chose a current source as the source, but you could just as easily make it a 100V source, and all voltages would be the same.

EDIT: In the vector diagram, VL and VC cancel.

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