For given circuit, does the current “io” through the branch equal zero after short circuit ? [2-port network]

The circuit is; simulate this circuit – Schematic created using CircuitLab

For given 2 port network, Im shorting V1 to solve for y22 and y12 and apply a current source at V2.[Y-Parameters]

This is the circuit we get; simulate this circuit

Now my question is; what will be io (current through 3-ohm resistor branch) will be equal to? Will it flow through 6-ohm resistor ? Or will it be equal to "zero"?

• If you include R1 in your circuit diagram, in parallel with the short-circuit, what's the current through it? – Chu Dec 27 '18 at 14:05
• @Chu I believe the current will flow into least resistive path, in other words will ignore 3-Ohm resistor. – calculusnoob Dec 27 '18 at 14:07
• That's correct. – Chu Dec 27 '18 at 14:09
• @Chu So you are implying "io" will be equal to zero ? since "io" is the current through 3-ohm resistor. – calculusnoob Dec 27 '18 at 14:10
• Yes............ – Chu Dec 27 '18 at 14:12