LRC circuit

1. May 6, 2015

toothpaste666

2. Relevant equations
XL = ωL
XC = 1/ωC
Z= sqrt(R^2+(XL-XC)^2)
∅ = tan^-1(XL-XC/R)

3. The attempt at a solution

A) a)
Irms = Vrms/R = 100 V/400 Ω = .25 A
b) 1) V= Vrms =100 V
2) V = IrmsXL = IrmsωL = (.25)(1000)(.9) = 225 V
3) V= IrmsXC = Irms/ωC = (.25)/((1000)(2E-6)) = 125 V
4) this part I am not sure how to do.
5) V = IrmsZ = Irmssqrt(R^2+(XL-XC)^2) = (.25)sqrt(400^2 + (900 - 500)^2) = 141 V

c) ∅=tan^-1(XL-XC/R) = tan^-1(400/400) = 45°
it is positive so voltage leads

B) a) ω = 1/sqrt(LC) = 1/sqrt(.9(2E-6)) = 745 rad/sec
b) 1) still 100 V
2) V = IrmsXL = IrmsωL = (.25)(745)(.9) = 168 V
3) V = IrmsXC = Irms/ωC = (.25)/((745)(2E-6)) = 168 V
4) ???
5) V = IrmsZ = IrmsR = .25(400) = 100 V

I am not entirely confident I did all of these right. feedback would be greatly appreciated

2. May 6, 2015

donpacino

your part a is wrong. I=V/Z, with Z being the impedance of the circuit. Since it is an AC waveform, the inductor and capacitor will have some impedance

3. May 6, 2015

toothpaste666

so part a) would be I = V/Z = V/ sqrt(R^2 + (XL-XC)^2) = 100/sqrt(400^2 +(1000(.9-2E-6))^2) = .1 A ???

also would I be able to do part 4 using the formula V = IZ where the R in the formula for Z is set to 0?

4. May 6, 2015

donpacino

No.

What have you learned about AC circuits and inductors and capacitors?
Have you learned about the laplace transform yet?

5. May 6, 2015

toothpaste666

I haven't heard of the laplace transform. Both of the things I said are wrong? I am still wrong about part a) ?

6. May 6, 2015

donpacino

the resistance at any given frequency for these purposes can be seen below
inducotor: w*L
capacitor: 1/(w*L)

now the inductor, capacitor,and resistor.... are they in series or parallel?

7. May 6, 2015

8. May 6, 2015

toothpaste666

they are in series

9. May 6, 2015

donpacino

yup, so to find the total impedance, you add them together

10. May 6, 2015

toothpaste666

I = V/Z = V/ sqrt(R^2 + (XL+XC)^2)
???
so when they are in parallel it is
1/XL + 1/XC ??

My book says XL-XC where does this come from?

11. May 6, 2015

donpacino

somehow I missed your equations page. oops

I forgot you havent really learned that much about AC so they gave you the equations.

http://en.wikipedia.org/wiki/Complex_plane

There are two ways to express complex numbers, polar and rectangular notation.
sqrt(R^2 + (XL+XC)^2) essentially converts the rectangular notation to the magnitude of polar notation
and ∅ = tan^-1(XL-XC/R) converts it to the angle of polar notation

12. May 6, 2015

donpacino

in that case, the second answer you gave is correct

13. May 6, 2015

toothpaste666

the .1 A is correct for part a) ?

For part 4) is this a case where the Voltage oscillates?

14. May 6, 2015

donpacino

yes
do you mean finding the phase angle??
if yes then look at your equation for theta

15. May 7, 2015

toothpaste666

I mean to find the voltage across the LC part of the circuit (If I am understanding the question correctly)
Originally I was thinking of using the equation for Z with R = 0 or
Z = sqrt((XL-XC)^2)
and then using
V = IZ

16. May 7, 2015

toothpaste666

I am still trying to figure this out. Is this one of the cases where I have to use the formula for oscillating voltage? V=v0coswt ?

17. May 11, 2015

donpacino

recall each part has an impedance. you know what the impedance is

V=I*Z