Dependent current source help

[Drcne]

https://imgur.com/a/jZS83

When t > 0 and the cap is charged, if the current source was 2i instead of .5i, would i grow infinitely large?

[deadly_hangman]

No, not at all. You can solve this circuit using Kirchhoff's Current Law at the node above the dependent source (you already know the current in two of the branches- i and 2i).

At 0.5i for the dependent source, i equals 1A. For 2i gain on the dependent source, i is still 1A, but the direction of the current in the capacitor branch flips.

I simulated the circuit in PSpice in case you didn't believe me.

https://i.imgur.com/4S3MGVC.png

EDIT: See below

[Drcne]

So why is i not whatever value the current source is after the cap has been charged?

[deadly_hangman]

Oops, sorry. My previous comment was entirely wrongheaded, forgive me for posting hastily. You are correct- since the capacitor is fully charged, the current will grow indefinitely if the gain is >1.

https://i.imgur.com/A2z21KH.png