Question

What would happen if no salt bridge were used in an electro chemical cell (like Zn-Cu cell)?

Answer 1

Without the salt bridge, the solution in the anode compartment would become positively charged and the solution in the cathode compartment would become negatively charged, because of the charge imbalance, the electrode reaction would quickly come to a halt.

Answer 2

the meta ions zn2+ formed by the loss of electrons will accumulate in one electrode and the negative ions so4 2+ will accumulate in the other. this the solution will develop charge and the current will stop following.
moreover the inner current will not be completed.