i am having trouble figuring out the voltage drops across individual components in a resonant circuit... the question is posted below. i have correctly computed the total current through the circuit, and i can correctly compute the resonant frequency.

here is what i have, i'll walk through my method for one of the AC frequencies in the table:
first i simplify based on the constants for all f -
Xl = (2 pi f L) = 2.073f
Xc = 1/(2 pi f C) = 15915/f

then work it out for the individual frequencies -
@50 Hz:
Xl = 103.65@90deg
Xc = 318.3@-90deg
Z = 214.65@-90deg. + 5@0deg. [5ohm resistor] = 214.708
I = E/Z = 250/214.708 = 1.16A

resonant freq:
f = sqrt(1/(2 pi L C)) = sqrt(7675.8) = 87.61Hz

but, i'm not sure where that puts me since according to the answers the voltages dropped do not seem to add up to 250. i guess that makes sense, since it's a resonant circuit, but given that i don't know how to calculate the drops across individual components. the answers show VERY small voltage drops across the inductor and capacitor. anybody know how to calculate this?

thanks a ton!

 

for starters, KVL states the voltage around a closed loop is zero. Stated another way Vsource = Vc + VL + Vr and its a series circuit so the current is the same throughout the circuit ( Ir = Ic = IL)

and VL and Vc oppose each other, so VL + (-Vc)

then add vectorally the voltage arcross the resistor

 

1st, find Zt, total impedance for each of the frequencies.

ill start with 50 Hz ZL = j104 Zc = -j318 Zr = 5

combining ZL and Zc = ZL + ZC = 104 + -j318 = -j214

Zt = sqrt(5sq + 214sq) = 214.05 -90deg

find I I = Vt/Zt 250mV 0deg / 214ohms -90deg = 1.168 mA +90deg

 

its been a while since i had to calculate that stuff, i hope i am correct, feel free to correct me if necessary

 

Attached is a plot of Vx and Vr and the resultant KVL summation done in Excel.

 

oh, holy crap. i just wasted your time guys, so sorry. i had just written this long post about how i totally didn't get it because it was a huge 250 volts and the total resistances would never add up since they weren't even a whole volt, but i'm a dumbass. it's 250*milli*V.

k, your work was exactly right, although i had put all the calculations for the total current in my original post. i was pretty pleased with myself that i figured out the pythagorean part too, and then my voltage drop calculations were way off because my decimal point on the total voltage was 3 places off so my totals were coming in looking way out of whack. i suck. i am still developing the "common sense" arm of my circuit analysis battle plan...

and thanks for the plot joe! that's great, what program is it?

 

The plot was made with Microsoft Excel, a spreadsheet, using their graphing routines.

My simulation program is TINA. I could have used the AC transfer function in the simulation program but I wanted to do it with the spreadsheet.