What is the steady-state value of the capacitor voltage

*v(infinity)*when excited by the unit step function source?

The way I went around the problem was to find ib(t) which is ib(t) = 5/(4 +1) = 1 A.

I then used the ib(t) to find the voltage source which would be the voltage at infinity (with the capacitor replaced by an open circuit)

Therefore the voltage should be V = 12ib(t) = 12 (1) = 12 V.

I was wrong and I'm not sure why.

Thanks.

PS: Was I wrong in assuming the Rth would be 100 ohms since the left half of the circuit would not contribute?