Solve Multiple RLC Problems: Currents & Voltages

[JasonHathaway]

Homework Statement

a)[/B] For the following circuit, if Vrms= 40V, write the current and the voltage equations.
http://www.imageupload.co.uk/images/2015/02/26/Captureaa814.png

b) For the following circuit, if i=0.8 sin(1000t-30), write the voltage equation and determine the average value of current.
http://www.imageupload.co.uk/images/2015/02/26/Capture2.png

Homework Equations

Ohm law for AC network.

The Attempt at a Solution

a) [/B] Vmax=Vrms/0.707=56.57 V
ZT=sqrt(R^2+XL^2)=12.72 ohms
Imax=Vmax/Z=4.44 A

So the equations would be:
i=Imax sin(wt) = 4.44 sin (wt)
v=Vmax sin(wt) = 56.57 sin(wt)

Should I write -90 or +90 since I'm dealing with inductor?

b) Since Imax=0.8 A, Vmax=Imax*ZT =0.8*5=4 (ZT=sqrt(R^2+(XL-XC)^2) =5)
v=4 sin(1000t-30)

Iavg=2*Imax/pi = 0.5 A (Or is it zero since we are dealing with sine wave?)

 

[BvU]

Hello Jason,

a) Neither -90 nor +90: it isn't a purely inductive load. Can you handle complex impedance ?

b) Again: there is a phase difference between V and I . Non-zero, because not resonant: X_L not equal to X_C
Average I zero ? true but corny.

 

[JasonHathaway]

a) Neither -90 nor +90: it isn't a purely inductive load. Can you handle complex impedance ?

I meant the equation for the voltage source itself.

b) Again: there is a phase difference between V and I . Non-zero, because not resonant: X_L not equal to X_C
Average I zero ? true but corny.

Also, I mean the equation for the source itself.
For the average value, should I dismiss 2*Imax/pi?

 

[jasonleroy]

Are you asking if the number you plug in for Vmax in problem "a" should have a phase angle associated with it? I would assume no. It would be explicitly stated in the problem.

 

[JasonHathaway]

Are you asking if the number you plug in for Vmax in problem "a" should have a phase angle associated with it? I would assume no. It would be explicitly stated in the problem.

OK. And for problem b)?

 

[BvU]

I maintain that the wording

write the current and the voltage equations

constitutes asking for amplitude and phase angle. The angle is pretty easy to solve with these values for $|Z_R|$ and $|Z_L|$ and you want to pay attention that you get the correct sign. b) idem.