What is the voltage across vc(0)?

[jofree87]

What is the voltage across v_c(0) in the diagram below?

The solution says its 10V but I don't know how they got that.

Through KVL, I got 0V.

Since all the current flows through the left most circuit, i_A = 10/1000 = .01A

3k and 1k(right) resistors have no current.

-10 + 1000i_A + v_c = 0

v_c = 0?

Am I doing something wrong here?

Edit: After applying nodal analysis, I got 10V, so I must be applying KVL wrong then?

 

[rpf_rr]

You are right, you can see why in another way, there are no corrents in vc and there is a short circuit beetween the nodes near vc, i.e. voltage=0, so vc must be zero