Solving RLC Circuit Response: Converting to Phasor Notation and Troubleshooting

[sdusheyko]

the problem statement is attached.

i've begun by converting everything into phasor notation but I'm not quite sure where to go from here. when i try to add the C and the L phasors, i get zero. this doesn't seem right.
another problem is i have no idea what to do when i get the impedances of the components added together. do i just add that to the input voltage for the answer?

any help appreciated.

 

[sdusheyko]

so I've converted the circuit to it's current source equivalent ( i can't remember if that's called thevenin or norton) and am able to add the impedances.

what to do from here?

i think I'm supposed to add the component impedances to the voltage input signal impedance and plug into v=ir for the voltage. but maybe not... I'm lost like i said. am i on the right track or far from it?

 

[UR_Correct]

Yes, you have to go into the frequency domain. From here, you can treat all the components like they're resistors with their respective impedances

So, yeah. For your source, you have 2 at an angle -pi/4. Impedance of Res, cap and inductor are 1, -j, and j, respectively (i.e., Zc = -j/(wC))

Now you just have to do circuit analysis from here. How can you get y(t)? Since voltages are the same in parallel, what if we combine the inductor and cap?

-j // j = ([-j]*[j])/(j-j) = undefined.

Well that's weird. I'm not sure what that means physically. I was going to combine those two components and then use voltage division across the equivalent impedance there. Ask your teacher about this. Maybe try to do a node equation?

 

[vela]

What you're finding is that when ω=1000, the LC combination has infinite impedance because that's the resonance frequency of the circuit. No current can flow, so the entire input voltage appears at the output.