How does a parallel circuit change when a branch is added?

the total resistance increases, so the current in the circuit decreases.
the total resistance decreases, so the current in the circuit increases.
the total resistance increases, so bulbs shine at a lower brightness.
the total resistance decreases, so bulbs shine at a higher brightness.

The correct answer is:

The total resistance decreases, so the current in the circuit increases.

In fact, the total resistance of a circuit is given by

if we add a branch in the circuit, we add a new term 1/R in the previous expression (where R is the resistance of the new branch), so we see that the term increases, therefore the total resistance decreases.

However, the current in the circuit is given by Ohm's law:

where V is the voltage provided by the battery. Therefore, since RT decreases, the current I will increase.

this is poiselle's equation from fluid mechanic in physics. mech eng