Principles of Electronics Question Parallel Circuits
You are assuming a constant current source and no load on each branch.  In that case yes your answer would be right.

However, consider this circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

The current through any one resistor (or branch of the circuit) will be \$I=V/R = 10/1000 = 0.01\$

The total current drawn from the power supply will of course be 4x that since there are 4 branches, all at 10mA.

Now, remove one branch, and what happens?  Each branch still has \$I=V/R = 10/1000 = 0.01\$ since that hasn't changed at all.  What has changed though is the total current.  Since there are now only 3 branches the total current drops to 30mA, as that is 3 x 0.01.

The only ways the current through any branch could change is if a) the resistance in that one branch changes, or b) the voltage of the power source changes.