How to Simplify a Frequency Response Circuit for Impedance Calculation?

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Marcin H
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Homework Statement


Circuit schematic with a current source f(t) in parallel with a 1 ohm resistor, followed by a series 1 ohm resistor and 3H inductor, feeding a 2F capacitor with output voltage y(t) across it. Problem text above reads: 5. In the following circuit, the input is f(t) = 1 + cos(t) + 2cos(2t). Determine the steady-state output y(t) of the circuit.


Homework Equations


V=IR
H(w) = Y/F = Impedance of circuit

The Attempt at a Solution



I wanted to simplify this circuit before I find any impedance, but I am not sure if I did my source transformation correctly. Can i combine the f(t) current source with the 1ohm in parallel even though there is another resistor in series with it? Or are my steps correct?

Handwritten circuit diagrams on lined paper: an original circuit with a current source f(t), 1 ohm resistors, a 3 H inductor and 2 F capacitor with output y(t), followed by source-transformed versions and a phasor-domain circuit with 2, 3j and 1/2j impedances.
 

Discussion

A resistor (or any passive component) in series with a current source has no effect outside of altering the potential differences on components within the current source branch. The branch will still deliver the current source's specified current with or without series resistance in the way; the current source will just alter its own potential difference to compensate and maintain the current.

What this means is that you can remove that series resistor entirely without making any change to the way the rest of the circuit operates.
 
gneill said:
What this means is that you can remove that series resistor entirely without making any change to the way the rest of the circuit operates.

So do I just ignore that resistor from the start or do I have to include it like I did in my source transformation?
 
Marcin H said:
So do I just ignore that resistor from the start or do I have to include it like I did in my source transformation?
Remove it. Erase it. Obliterate it. Pretend it never exited :smile::biggrin:
 
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gneill said:
Remove it. Erase it. Obliterate it. Pretend it never exited :smile::biggrin:
Lol.. Thanks! :smile:
 

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